Merge origin master (Mega-squash); keep the rewrite.

`snapshot` writes each tracked model's forecast quantiles at the seven
backtest horizons from the latest price to data/forecasts/<origin>.csv. It
refuses stale data (older than two days) and duplicate dates, so snapshots
can't be reconstructed after the fact; committing them dates them.
`forward` scores every recorded forecast whose target date has passed,
reusing the backtest's scoring (now factored out as evaluate.score).

Tracked: random_walk, drift_rw, cycle, powerlaw, plus powerlaw_ou,
powerlaw_ou_param and cycle_on_powerlaw, which development data couldn't
settle. `just weekly` runs update, snapshot and forward.

First snapshot: 2026-09-23 (BTC $84.4K). The first outcomes are due
2026-10-23.

.gitignore

@@ -1,5 +1,8 @@
-bitcoin_*.png
-bitcoin_*.txt
 /output
+__pycache__/
+.pytest_cache/
+.ruff_cache/
+.venv/
+result
 scratch.py
-/.private
+.DS_Store

NOTES.md

@@ -1,361 +0,0 @@
-# Bitcoin Price Model Documentation
-
-## Model Overview
-A probabilistic price projection model combining log returns analysis, cycle awareness, and Monte Carlo simulation. The model generates projected price ranges with confidence intervals, balancing short-term market dynamics with long-term cyclical patterns.
-
-## Core Design Principles
-
-### 1. Return Analysis
-- Uses log returns for better handling of exponential growth
-- Combines multiple timeframes for volatility estimation
-- Implements adaptive window sizing based on market conditions
-- Handles volatility clustering through regime-aware adjustments
-
-### 2. Cycle Integration
-- Recognizes Bitcoin's ~4 year (1460 day) halving cycle
-- Maps historical returns to cycle positions (0-1 scale)
-- Adjusts expectations based on position in cycle
-- Handles transitions between cycles with uncertainty scaling
-
-### 3. Market Era Recognition
-Three distinct eras with specific characteristics:
-- Early (2013-2017): Higher base volatility, conservative trends
-- Transition (2017-2020): Futures market introduction period
-- Mature (2020+): Institutional participation, reduced base volatility
-
-### 4. Uncertainty Estimation
-- Generates both point estimates and confidence intervals
-- Adapts uncertainty based on market conditions
-- Uses asymmetric volatility response
-- Implements dynamic confidence interval calibration
-
-## Architecture
-
-### Key Components
-1. **Trend Analysis (`analyze_trends`)**
-   - Calculates cycle-position-specific returns
-   - Applies position-aware smoothing
-   - Handles cycle boundaries
-
-2. **Volatility Estimation (`calculate_volatility`)**
-   - Adaptive window sizing
-   - Multi-timeframe integration
-   - Era-specific scaling
-   - Regime detection and response
-
-3. **Price Projection (`project_prices`)**
-   - Monte Carlo simulation engine
-   - Dynamic uncertainty scaling
-   - Confidence interval calculation
-   - Trend integration
-
-4. **Projection Adjustment (`get_projection_adjustments`)**
-   - Time-varying uncertainty scaling
-   - Market condition response
-   - Cycle position awareness
-   - Minimum uncertainty bounds
-
-# Model Performance & Validation
-
-## Performance Characteristics
-
-### Normal Market Conditions
-- MAPE: 30-40% typical
-- 95% CI Coverage: ~95%
-- 68% CI Coverage: ~73%
-- Best performance in mature market periods (2020+)
-- Most reliable for 3-6 month horizons
-
-### Stress Periods
-- MAPE: 30-60%
-- 95% CI Coverage: ~95%
-- 68% CI Coverage: ~76%
-- Wider but well-calibrated confidence intervals
-- Maintains reliability through increased uncertainty
-
-### Key Strengths
-1. Consistent confidence interval coverage
-2. Rapid adaptation to volatility changes
-3. Robust handling of cycle transitions
-4. Well-calibrated uncertainty estimates
-
-### Known Limitations
-1. Higher error during market structure changes
-2. Increased uncertainty in early cycle periods
-3. Limited incorporation of external factors
-4. May underestimate extreme events
-
-## Validation Framework
-
-### Backtest Configuration
-- Minimum training period: 8 years
-- Validation period: 2 years
-- Rolling window approach
-- Separate evaluation of normal/stress periods
-
-### Key Test Periods
-1. **Cycle Transitions**
-   - Pre/post halving periods
-   - Historical halvings (2016, 2020, 2024)
-   - Cycle peak/trough transitions
-
-2. **Market Structure Changes**
-   - Futures introduction (2017)
-   - Institution adoption (2020-2021)
-   - Major market events (e.g., COVID crash)
-
-3. **Recent History**
-   - 2021 bull market
-   - 2022 drawdown
-   - 2024 recovery
-
-### Validation Metrics
-1. **Accuracy Measures**
-   - MAPE (Mean Absolute Percentage Error)
-   - RMSE (Root Mean Square Error)
-   - Maximum deviation
-
-2. **Calibration Measures**
-   - Confidence interval coverage
-   - Uncertainty estimation accuracy
-   - Regime transition handling
-
-3. **Stability Measures**
-   - Parameter sensitivity
-   - Training period dependence
-   - Regime change response
-
-# Technical Implementation
-
-## Core Functions
-
-### Volatility Calculation
-```python
-def calculate_volatility(df, short_window=30, medium_window=90, long_window=180):
-    """
-    Adaptive volatility calculation combining multiple timeframes.
-
-    Features:
-    - Dynamic window sizing based on market conditions
-    - Era-specific scaling factors
-    - Regime-aware adjustments
-    - Robust error handling and fallbacks
-    """
-```
-
-Key parameters:
-- `short_window`: Fast response (default 30 days)
-- `medium_window`: Primary estimate (default 90 days)
-- `long_window`: Stability baseline (default 180 days)
-
-Adaptive features:
-- Windows shrink in high volatility periods
-- Expand during low volatility
-- Minimum size constraints for stability
-- Weighted combination based on regime
-
-### Cycle Position
-```python
-def get_cycle_position(date, halving_dates):
-    """
-    Calculate position in halving cycle (0 to 1).
-    0 = halving event
-    1 = just before next halving
-    """
-```
-
-Position calculation:
-- Linear interpolation between halvings
-- Special handling for pre-first-halving
-- Extension mechanism for future cycles
-- Built-in boundary condition handling
-
-### Price Projection
-```python
-def project_prices(df, days_forward=365, simulations=1000,
-                  confidence_levels=[0.95, 0.68]):
-    """
-    Generate price projections with confidence intervals.
-
-    Core simulation parameters:
-    - Number of paths: 1000
-    - Confidence levels: 95% and 68%
-    - Dynamic uncertainty scaling
-    """
-```
-
-## Data Requirements
-
-### Input Data
-Minimum fields:
-- Date
-- Close price
-- Trading volume (optional)
-- High/Low (optional)
-
-Format requirements:
-- Daily data preferred
-- Sorted chronologically
-- No missing dates
-- Prices > 0
-
-### Training Data
-Minimum requirements:
-- 2 years for basic operation
-- 8 years recommended
-- Must include at least one cycle transition
-- Should span multiple market regimes
-
-## Error Handling
-
-### Data Validation
-- Missing value detection and interpolation
-- Outlier identification
-- Zero/negative price handling
-- Volume anomaly detection
-
-### Runtime Guards
-- Minimum data length checks
-- Window size validation
-- Numerical stability checks
-- Regime transition handling
-
-### Fallback Mechanisms
-1. Simple volatility calculation
-2. Default uncertainty estimates
-3. Conservative parameter sets
-4. Standard cycle assumption
-
-## Memory and Performance
-
-### Optimization Features
-- Efficient numpy operations
-- Vectorized calculations where possible
-- Smart data windowing
-- Caching of intermediate results
-
-### Resource Usage
-Typical requirements for 10-year dataset:
-- Memory: ~100MB
-- CPU: ~2-5 seconds per projection
-- Storage: Negligible
-
-### Parallelization
-- Multiprocessing support for backtests
-- Independent path simulation
-- Multiple period analysis
-- Backtest parallelization
-
-# Development History & Evolution
-
-## Major Versions
-
-### Version 1.0 (Initial Implementation)
-- Basic log return analysis
-- Fixed volatility windows
-- Simple cycle position calculation
-- Base Monte Carlo simulation
-
-### Version 2.0 (Market Structure)
-- Added era-based adjustments
-- Improved cycle handling
-- Multiple timeframe volatility
-- Enhanced Monte Carlo engine
-
-### Version 3.0 (Current)
-- Adaptive volatility windows
-- Dynamic uncertainty scaling
-- Improved regime detection
-- Enhanced confidence interval calibration
-
-## Key Improvements
-
-### Volatility Estimation
-1. **Fixed → Adaptive Windows**
-   - Initial: Fixed 30/90/180 day windows
-   - Current: Dynamic sizing based on regime
-   - Result: Better regime transition handling
-
-2. **Uncertainty Calibration**
-   - Initial: Fixed scaling factors
-   - Current: Market-aware dynamic scaling
-   - Result: More reliable confidence intervals
-
-3. **Era Recognition**
-   - Initial: Single model for all periods
-   - Current: Era-specific adjustments
-   - Result: Better handling of market evolution
-
-### Simulation Engine
-1. **Path Generation**
-   - Initial: Basic random walks
-   - Current: Regime-aware path simulation
-   - Result: More realistic price trajectories
-
-2. **Confidence Intervals**
-   - Initial: Fixed width
-   - Current: Dynamic, asymmetric intervals
-   - Result: Better calibrated uncertainty
-
-## Failed Experiments
-
-### 1. Complex Regime Detection
-- Attempted multiple indicator fusion
-- Added excessive complexity
-- Reduced model stability
-- Reverted to simpler approach
-
-### 2. Machine Learning Integration
-- Tested neural network components
-- Reduced interpretability
-- Inconsistent improvements
-- Kept traditional statistical approach
-
-### 3. External Factor Integration
-- Tried incorporating macro indicators
-- Added noise to projections
-- Complicated parameter estimation
-- Maintained focus on price dynamics
-
-## Recent Improvements (2024)
-
-### Adaptive Volatility Windows
-- Implementation: Dynamic window sizing
-- Purpose: Better regime handling
-- Results:
-  - Improved 95% CI coverage to ~95%
-  - Better stress period handling
-  - More reliable uncertainty estimates
-
-### Performance Metrics
-Normal Periods:
-- MAPE: 39.9%
-- RMSE: $12,007
-- 95% CI Coverage: 95.9%
-- 68% CI Coverage: 72.5%
-
-Stress Periods:
-- MAPE: 32.8%
-- RMSE: $12,794
-- 95% CI Coverage: 95.2%
-- 68% CI Coverage: 76.1%
-
-## Future Directions
-
-### Short Term
-1. Fine-tune adaptive parameters
-2. Improve transition period handling
-3. Enhanced backtest framework
-4. Additional regime indicators
-
-### Medium Term
-1. Cycle strength indicators
-2. Volume analysis integration
-3. Improved documentation
-4. Performance optimization
-
-### Long Term
-1. Real-time adaptation framework
-2. Advanced regime detection
-3. Market microstructure integration
-4. External API integration

README.md

@@ -6,18 +6,178 @@
 
 **Don't take this seriously. It's all in good fun.**
 
-I decided to have fun and ask Anthropic's Claude AI (3.6 Sonnet) to help build
+## The 2024 edition
-a Bitcoin price model, using data from [Investing.com](https://www.investing.com/crypto/bitcoin/historical-data).
 
-The model is still a mess: lots of redundant code as we went through various
+In November 2024 I asked Claude (3.6 Sonnet, via copy and paste in Claude Web)
-methods for projecting future prices; the plots' colors don't render correctly.
+to help build a Bitcoin price model. After a lot of branching it produced ~2000
+lines of cycle analysis, "market fundamentals", era adjustments and Monte Carlo,
+and forecasts like this one (as of 2024-11-14):
 
-I feel like I'm dangerous enough to know what to ask for out of a model, but
+![moooooon](docs/2024-forecast.png)
-not knowledgeable enough evaluate whether what Claude produced actually makes
-any sense. (Stats class in college was a long time ago...)
 
-## tl;dr show me the projection!
+In September 2026 a newer Claude scored the forecasts it made on 2024-11-27
+against what actually happened:
 
-As of writing (2024-11-14), here is what the model generates:
+| | 2024 forecast (median) | Actual |
+|---|---|---|
+| Cycle top | 2025-10-21, $199K | 2025-10-06, $124.7K |
+| 2026-06-30 | $133K (95% floor $65K) | $58.5K |
+| 2026-09-23 | $124K | $84.4K |
 
-![moooooon](./moneyshot.png)
+It called the timing of the top within 15 days, 19 months ahead, but put the
+level ~60% too high. "The price stays at $92.7K" was a better forecast (18%
+mean error against 68%). Its "95%" intervals were really ~81% intervals past a
+year out, thanks to a fudge factor that narrowed them at long horizons.
+
+That code lives in the jj/git history. This is the rewrite.
+
+## How it works now
+
+A forecast is a probability distribution of the price at each horizon, not a
+line. Every model produces quantiles of log price, and every model is scored
+the same way:
+
+- **Walk-forward.** Every 30 days from 2014 on, each model sees only the data up
+  to that day and forecasts 1 month to 4 years ahead.
+- **CRPS.** Each forecast is scored against what happened with the continuous
+  ranked probability score, in log-price units (0.1 ≈ "typically 10% off"). It
+  rewards being sharp and being calibrated at once, and can't be gamed by
+  narrowing or widening intervals.
+- **Baselines.** Skill is reported relative to a zero-drift random walk, with a
+  90% block-bootstrap interval. Nearby forecasts overlap heavily, so the report
+  also shows `windows`: the number of genuinely independent outcomes.
+- **Holdout.** Development only sees data up to 2024-11-26, the last day the
+  2024 model saw. Everything after it is held out, and is scored only by
+  `just holdout`, once per round of model changes. (Caveat: we already know
+  roughly what happened in 2025-26, so it isn't perfectly blind.)
+
+### Models
+
+- `random_walk`: zero drift; "it stays about here, give or take".
+- `drift_rw`: drift equal to the last four years' average; "it keeps doing what
+  it did last cycle".
+- `cycle`: the 2024 model's one real idea. Expected return depends on the day of
+  the halving cycle, estimated from past cycles, with recent cycles weighted
+  more.
+- `powerlaw`: log price grows linearly in log time since genesis, so growth
+  keeps slowing. Fitted walk-forward; the exponent has stayed between 5.4 and
+  6.0 in every fit since 2014.
+
+### Findings so far (development data)
+
+- `cycle` loses to the random walk at every horizon, and so does every setting
+  tried (recency half-life 0.25-2 cycles, smoothing bandwidth 15-60 days).
+  The level is the problem: each cycle has grown less than the last (log
+  return 4.0, 2.6, 2.0, i.e. roughly ×55, ×13, ×7), so any average of past
+  cycles overshoots.
+- `powerlaw` models exactly that, and it is the first model to beat the random
+  walk with some confidence: +53% and +63% skill at 3 and 4 years, with
+  unbiased outcomes (mean PIT 0.51). Only 3-4 independent windows back that
+  up, the functional form is famous *because* it fits Bitcoin's history, and
+  the holdout hasn't been run yet.
+- Its intervals are too wide at long horizons (the 80% interval held every
+  3-year outcome), because it treats deviations from the trend as permanent.
+
+### A/B tests of the 2024 ideas
+
+`just ab` runs the experiments in `btcmodel/experiments.py`: ideas salvaged
+from the old branches (catalogued in [docs/2024-ideas.md](docs/2024-ideas.md)),
+each a control plus variants that change one component. Hypotheses and the
+verdict rule were written down before anything ran. With ~100 comparisons,
+expect a few flukes either way.
+
+| Experiment | Idea | Verdict |
+|---|---|---|
+| shrink-cycle | scale the cycle drift by 0.25/0.5/0.75 | better, all three: it fixes the level crudely |
+| diminishing-returns | power-law trend, optionally reverting to it, or the cycle shape rescaled to it | better (both power-law variants); cycle shape on the power law inconclusive |
+| vol-window | EWMA blends, shorter or longer windows | worse: the plain 365-day window wins |
+| vol-reversion | volatility reverting to a long-run level or falling trend | worse |
+| cycle-vol | volatility by cycle position | inconclusive (no effect) |
+| tails | Student-t, or empirical horizon-level shape | Student-t worse; empirical +5% at 1 month only |
+| cycle-phase | align cycles by fraction elapsed, not days | inconclusive |
+
+Round 2 tested the power law against two refinements (the verdict rule was
+unchanged, and the holdout candidates were fixed before it ran):
+
+| Experiment | Idea | Verdict |
+|---|---|---|
+| powerlaw-ou | deviations from the trend revert, so uncertainty levels off; optionally plus trend-parameter uncertainty | inconclusive: +21% to +45% at 2-4 years (intervals above zero), but -0.3% and -1% at 1 month fail the "never negative" clause. Bands too narrow without parameter uncertainty, too wide with it |
+| cycle-on-powerlaw | the cycle's timing, rescaled to the power-law level | inconclusive: +18% at 2 years, slightly negative at short horizons and 4 years |
+
+### Holdout (run once, 2026-09-24)
+
+Scored on outcomes after 2024-11-26 for the four candidates fixed in advance
+(`random_walk`, `drift_rw`, `cycle`, `powerlaw`). The holdout is ~22 months
+long, so at 2-4 years it is essentially one outcome period seen from several
+origins (1.4-1.9 windows), and the bootstrap intervals there mean little.
+
+| Skill vs random walk | 1mo | 3mo | 6mo | 1y | 2y | 3y | 4y |
+|---|---|---|---|---|---|---|---|
+| drift_rw | -0% | +1% | +5% | +14% | +31% | +53% | -65% |
+| cycle | -14% | -8% | -25% | -104% | -46% | -21% | -179% |
+| powerlaw | -1% | -7% | -5% | +3% | +45% | +58% | +15% |
+
+Consistent with development: nothing beats the random walk inside a year,
+`cycle` fails badly, and `powerlaw` is the best long-horizon forecast, unbiased
+at 2-3 years (mean PIT 0.53-0.56) but with intervals too wide (its 80% interval
+held every 2- and 3-year outcome). The holdout is now spent for these models;
+a new model needs new data to be tested honestly.
+
+### Forward test (from 2026-09-23)
+
+New data is the only honest test left, so forecasts are now recorded before
+their outcomes exist. `just snapshot` writes every tracked model's forecast
+from the latest price to `data/forecasts/<date>.csv`. It refuses if the price
+data is more than two days old or the date already has a snapshot, and the
+files are committed so version control dates them. `just forward` scores
+every recorded forecast whose target date has passed, the same way the
+backtest does.
+
+Tracked: the four registered models plus `powerlaw_ou`, `powerlaw_ou_param`
+and `cycle_on_powerlaw`, which development data couldn't settle. Snapshots
+store the forecasts themselves, so if a model's definition changes it gets a
+new name. The routine is `just weekly` (update, snapshot, score), then commit
+the new snapshot. The first 1-month outcomes arrive 2026-10-23; 1-year results
+need until late 2027, and 4-year ones until 2030.
+
+## Usage
+
+With Nix:
+
+```sh
+nix develop
+just update     # fetch new daily prices from Coinbase
+just backtest   # score models on development data -> output/backtest/
+just forecast   # forecast from the latest price -> output/forecast/
+just ab         # run A/B experiments -> output/ab/
+just weekly     # new prices, a forward-test snapshot, and its scores so far
+just test
+just holdout    # score on held-out outcomes; sparingly
+```
+
+Without Nix, any Python 3.13 with numpy, pandas 3, scipy and matplotlib works:
+`python -m btcmodel --help`.
+
+## Layout
+
+```
+btcmodel/
+  data.py       price loading (Investing.com archive + Coinbase), dev cutoff
+  halving.py    halving calendar, position in cycle
+  forecast.py   Forecast (quantiles of log price), CRPS, PIT
+  evaluate.py   walk-forward backtest and summary
+  experiments.py  A/B tests: hypothesis, control, variants, verdict rule
+  forward.py    forward test: record forecasts, score them as outcomes arrive
+  models/       drift, volatility and shape components; register models in __init__.py
+  plots.py      fan chart, skill and calibration charts
+```
+
+A model is any object with a `name` and
+`forecast(history, horizons) -> Forecast`. `history` is a date-indexed frame
+holding everything up to the forecast origin and nothing after it. Other data
+sources (hash rate, on-chain metrics, macro series) can join it as extra
+columns. Anything published with a lag must be shifted to the date it was
+actually available, or the backtest will quietly cheat.
+
+Price data: [Investing.com](https://www.investing.com/crypto/bitcoin/historical-data)
+through 2024-11-26, then Coinbase Exchange daily closes (UTC).

btcmodel/__main__.py

@@ -0,0 +1,190 @@
+"""
+Command line entry point.
+
+    python -m btcmodel update              fetch new daily prices from Coinbase
+    python -m btcmodel backtest            score models on development data
+    python -m btcmodel backtest --holdout  score models on outcomes after DEV_CUTOFF
+    python -m btcmodel forecast            forecast from the latest price
+    python -m btcmodel ab [NAME ...]       run A/B experiments on development data
+    python -m btcmodel snapshot            record tracked models' forecasts for the forward test
+    python -m btcmodel forward             score recorded forecasts whose targets have passed
+"""
+
+import argparse
+from pathlib import Path
+
+import numpy as np
+import pandas as pd
+
+from . import data, evaluate, experiments, forward, plots
+from .models import MODELS
+
+FORECAST_REPORT_HORIZONS = (182, 365, 730, 1095, 1460)
+FORECAST_REPORT_LEVELS = (0.05, 0.25, 0.5, 0.75, 0.95)
+
+
+def main() -> None:
+    parser = argparse.ArgumentParser(prog="btcmodel", description="Bitcoin price model")
+    parser.add_argument("-o", "--output", type=Path, default=Path("output"))
+    parser.add_argument("-m", "--models", nargs="+", choices=list(MODELS), default=list(MODELS))
+    commands = parser.add_subparsers(dest="command", required=True)
+    commands.add_parser("update", help="fetch new daily prices")
+    backtest = commands.add_parser("backtest", help="walk-forward evaluation")
+    backtest.add_argument(
+        "--holdout",
+        action="store_true",
+        help=f"score outcomes after {data.DEV_CUTOFF:%Y-%m-%d} (don't use while developing)",
+    )
+    commands.add_parser("forecast", help="forecast from the latest price")
+    ab = commands.add_parser("ab", help="run A/B experiments on development data")
+    ab.add_argument("names", nargs="*", help="experiments to run (default: all)")
+    commands.add_parser("snapshot", help="record forecasts for the forward test")
+    commands.add_parser("forward", help="score recorded forecasts")
+    args = parser.parse_args()
+    if args.command == "ab" and (unknown := set(args.names) - set(experiments.EXPERIMENTS)):
+        parser.error(f"unknown experiments: {', '.join(sorted(unknown))}")
+    models = [MODELS[name] for name in args.models]
+
+    if args.command == "update":
+        added = data.update_coinbase()
+        print(f"added {added} days; latest {data.load_prices().index[-1]:%Y-%m-%d}")
+    elif args.command == "backtest":
+        run_backtest(models, args.output, args.holdout)
+    elif args.command == "forecast":
+        run_forecast(models, args.output)
+    elif args.command == "ab":
+        run_ab(args.names or list(experiments.EXPERIMENTS), args.output)
+    elif args.command == "snapshot":
+        run_snapshot()
+    elif args.command == "forward":
+        run_forward(args.output)
+
+
+def run_backtest(models, output: Path, holdout: bool) -> None:
+    if holdout:
+        name, prices = "holdout", data.load_prices()
+        scores = evaluate.backtest(models, prices, score_after=data.DEV_CUTOFF)
+    else:
+        name, prices = "backtest", data.load_prices(until=data.DEV_CUTOFF)
+        scores = evaluate.backtest(models, prices)
+    out = output / name
+    out.mkdir(parents=True, exist_ok=True)
+
+    summary = evaluate.summarize(scores)
+    report = (
+        f"{name}: origins every {evaluate.ORIGIN_STEP_DAYS} days from "
+        f"{evaluate.FIRST_ORIGIN:%Y-%m-%d}, outcomes through {prices.index[-1]:%Y-%m-%d}\n\n"
+        + evaluate.format_summary(summary)
+    )
+    print(report)
+    (out / "report.txt").write_text(report + "\n")
+    scores.to_csv(out / "scores.csv", index=False)
+    summary.to_csv(out / "summary.csv", index=False)
+    plots.skill_chart(summary, out / "skill.png", f"{name}: skill by horizon")
+    plots.calibration_chart(summary, out / "calibration.png", f"{name}: interval coverage")
+    print(f"\nwrote {out}/")
+
+
+def run_ab(names: list[str], output: Path) -> None:
+    prices = data.load_prices(until=data.DEV_CUTOFF)
+    verdicts = []
+    for name in names:
+        experiment = experiments.EXPERIMENTS[name]
+        scores, summary = experiments.run(experiment, prices)
+        out = output / "ab" / name
+        out.mkdir(parents=True, exist_ok=True)
+        control = experiment.control.name
+        report = (
+            f"{name}: {experiment.hypothesis}\n(from {experiment.source})\n\n"
+            + evaluate.format_summary(summary, baseline=control)
+        )
+        print(report + "\n")
+        (out / "report.txt").write_text(report + "\n")
+        summary.to_csv(out / "summary.csv", index=False)
+        plots.skill_chart(summary, out / "skill.png", f"{name}: skill vs {control}", control)
+        plots.calibration_chart(summary, out / "calibration.png", f"{name}: interval coverage")
+        for variant in experiment.variants:
+            v = summary[summary.model == variant.name].set_index("horizon")
+            verdicts.append(
+                {
+                    "experiment": name,
+                    "variant": variant.name,
+                    "control": control,
+                    **{evaluate.horizon_label(h): f"{s:+.0%}" for h, s in v["skill"].items()},
+                    "verdict": experiments.verdict(v),
+                }
+            )
+    table = pd.DataFrame(verdicts).to_string(index=False)
+    print(table)
+    (output / "ab").mkdir(parents=True, exist_ok=True)
+    (output / "ab" / "verdicts.txt").write_text(table + "\n")
+
+
+def run_snapshot() -> None:
+    prices = data.load_prices()
+    path = forward.snapshot(prices)
+    recorded = [(m, f) for m, f in forward.load_snapshots() if f.origin == prices.index[-1]]
+    medians = pd.DataFrame(
+        {m: [plots.price_formatter(p) for p in np.exp(f.quantile(0.5))] for m, f in recorded},
+        index=[evaluate.horizon_label(h) for h in evaluate.HORIZONS],
+    ).T
+    print(
+        f"recorded {len(recorded)} models' forecasts from {prices.index[-1]:%Y-%m-%d} in {path}\n"
+    )
+    print("medians:\n" + medians.to_string())
+
+
+def run_forward(output: Path) -> None:
+    prices = data.load_prices()
+    scores = forward.score_snapshots(prices)
+    due = forward.next_due(prices)
+    if scores.empty:
+        when = f"; the first is due {due:%Y-%m-%d}" if due is not None else ""
+        print(f"no recorded forecast has reached its target date yet{when}")
+        return
+    out = output / "forward"
+    out.mkdir(parents=True, exist_ok=True)
+    summary = evaluate.summarize(scores, step_days=forward.SNAPSHOT_STEP_DAYS)
+    report = (
+        f"forward test: {scores.origin.nunique()} snapshots from {scores.origin.min():%Y-%m-%d}, "
+        f"outcomes through {prices.index[-1]:%Y-%m-%d}\n\n" + evaluate.format_summary(summary)
+    )
+    if due is not None:
+        report += f"\n\nnext outcome due {due:%Y-%m-%d}"
+    print(report)
+    (out / "report.txt").write_text(report + "\n")
+    scores.to_csv(out / "scores.csv", index=False)
+    summary.to_csv(out / "summary.csv", index=False)
+    plots.skill_chart(summary, out / "skill.png", "forward test: skill by horizon")
+    plots.calibration_chart(summary, out / "calibration.png", "forward test: interval coverage")
+    print(f"\nwrote {out}/")
+
+
+def run_forecast(models, output: Path) -> None:
+    prices = data.load_prices()
+    horizons = np.arange(1, max(FORECAST_REPORT_HORIZONS) + 1)
+    forecasts = {m.name: m.forecast(prices, horizons) for m in models}
+    out = output / "forecast"
+    out.mkdir(parents=True, exist_ok=True)
+
+    rows = []
+    for name, f in forecasts.items():
+        for h in FORECAST_REPORT_HORIZONS:
+            row = {"model": name, "date": f.dates[h - 1].date(), "horizon": h}
+            for level in FORECAST_REPORT_LEVELS:
+                row[f"p{level * 100:02.0f}"] = np.exp(f.quantile(level)[h - 1])
+            rows.append(row)
+    table = pd.DataFrame(rows)
+    table.to_csv(out / "forecast.csv", index=False)
+
+    shown = table.copy()
+    for column in shown.columns[3:]:
+        shown[column] = shown[column].map(plots.price_formatter)
+    print(f"from {prices.index[-1]:%Y-%m-%d} at {plots.price_formatter(prices.close.iloc[-1])}\n")
+    print(shown.to_string(index=False))
+    plots.fan_chart(prices, forecasts, out / "fan.png")
+    print(f"\nwrote {out}/")
+
+
+if __name__ == "__main__":
+    main()

btcmodel/data.py

@@ -0,0 +1,117 @@
+"""Daily BTC-USD closing prices.
+
+Two sources, stitched at ARCHIVE_END:
+
+- data/investing.csv: the original Investing.com download (2010-07-18 onward).
+  Its last row (2024-11-27) was an intraday snapshot, so it is cut a day early.
+- data/coinbase.csv: Coinbase Exchange daily candles (UTC days), appended by
+  `python -m btcmodel update`.
+
+Everything up to ARCHIVE_END is development data. Everything after it is the
+holdout: outcomes nobody had seen while the 2024 model was being built, and which
+model development here must not look at (see evaluate.py).
+"""
+
+import datetime as dt
+import json
+import urllib.request
+from pathlib import Path
+
+import numpy as np
+import pandas as pd
+
+DATA_DIR = Path(__file__).resolve().parent.parent / "data"
+ARCHIVE_CSV = DATA_DIR / "investing.csv"
+COINBASE_CSV = DATA_DIR / "coinbase.csv"
+
+ARCHIVE_END = pd.Timestamp("2024-11-26")
+DEV_CUTOFF = ARCHIVE_END
+
+# 2010 has four distinct prices and no change on 89% of days; it is noise.
+DATA_START = pd.Timestamp("2011-01-01")
+
+COINBASE_URL = "https://api.exchange.coinbase.com/products/BTC-USD/candles"
+COINBASE_MAX_CANDLES = 300
+
+
+def load_prices(
+    until: pd.Timestamp | str | None = None, start: pd.Timestamp | str = DATA_START
+) -> pd.DataFrame:
+    """
+    Load daily closes as a frame indexed by date, with a single `close` column.
+
+    Models receive a prefix of this frame, so additional data sources can be
+    joined in as extra columns later without changing the model interface.
+    """
+    archive = _read_archive()
+    parts = [archive[archive.index <= ARCHIVE_END]]
+    if COINBASE_CSV.exists():
+        coinbase = pd.read_csv(COINBASE_CSV, index_col="date", parse_dates=["date"])
+        parts.append(coinbase.loc[coinbase.index > ARCHIVE_END, ["close"]])
+    df = pd.concat(parts).sort_index()
+
+    df = df[df.index >= pd.Timestamp(start)]
+    if until is not None:
+        df = df[df.index <= pd.Timestamp(until)]
+
+    expected = pd.date_range(df.index[0], df.index[-1], freq="D")
+    missing = expected.difference(df.index)
+    if len(missing):
+        raise ValueError(f"{len(missing)} missing days, first {missing[0].date()}")
+    if not (df["close"] > 0).all():
+        raise ValueError("non-positive closing price")
+    return df
+
+
+def log_returns(df: pd.DataFrame) -> pd.Series:
+    """Daily log returns of the close, without the leading NaN."""
+    return np.log(df["close"]).diff().iloc[1:]
+
+
+def _read_archive() -> pd.DataFrame:
+    raw = pd.read_csv(ARCHIVE_CSV, encoding="utf-8-sig", thousands=",")
+    dates = pd.to_datetime(raw["Date"], format="%m/%d/%Y")
+    return pd.DataFrame({"close": raw["Price"].astype(float).values}, index=dates.rename("date"))
+
+
+def update_coinbase() -> int:
+    """Append completed daily candles since the last stored day. Returns rows added."""
+    if COINBASE_CSV.exists():
+        existing = pd.read_csv(COINBASE_CSV, index_col="date", parse_dates=["date"])
+        first = existing.index.max() + pd.Timedelta(days=1)
+    else:
+        existing = None
+        first = ARCHIVE_END + pd.Timedelta(days=1)
+    # Today's candle is still forming; only take finished UTC days.
+    last = pd.Timestamp(dt.datetime.now(dt.UTC).date()) - pd.Timedelta(days=1)
+
+    rows = []
+    chunk_start = first
+    while chunk_start <= last:
+        chunk_end = min(chunk_start + pd.Timedelta(days=COINBASE_MAX_CANDLES - 1), last)
+        rows.extend(_fetch_candles(chunk_start, chunk_end))
+        chunk_start = chunk_end + pd.Timedelta(days=1)
+    if not rows:
+        return 0
+
+    new = pd.DataFrame(rows, columns=["date", "close"]).set_index("date").sort_index()
+    new = new[(new.index >= first) & (new.index <= last)]
+    combined = new if existing is None else pd.concat([existing, new])
+    combined = combined[~combined.index.duplicated(keep="last")].sort_index()
+    combined.to_csv(COINBASE_CSV, date_format="%Y-%m-%d")
+    return len(new)
+
+
+def _fetch_candles(start: pd.Timestamp, end: pd.Timestamp) -> list[tuple[pd.Timestamp, float]]:
+    url = (
+        f"{COINBASE_URL}?granularity=86400"
+        f"&start={start:%Y-%m-%d}T00:00:00Z&end={end:%Y-%m-%d}T00:00:00Z"
+    )
+    # Coinbase rejects requests without a User-Agent.
+    request = urllib.request.Request(url, headers={"User-Agent": "btcmodel"})
+    with urllib.request.urlopen(request, timeout=30) as response:
+        candles = json.load(response)
+    # Each candle is [time, low, high, open, close, volume].
+    return [
+        (pd.Timestamp(dt.datetime.fromtimestamp(c[0], dt.UTC).date()), float(c[4])) for c in candles
+    ]

btcmodel/evaluate.py

@@ -0,0 +1,133 @@
+"""
+Walk-forward evaluation.
+
+From each origin (every ORIGIN_STEP_DAYS from FIRST_ORIGIN), each model sees the
+data up to that day only and forecasts every horizon. Each forecast whose target
+date has been observed is scored against what happened.
+
+Development runs load data only up to DEV_CUTOFF, so outcomes after it cannot
+influence model design. The holdout run scores only targets after DEV_CUTOFF.
+"""
+
+import numpy as np
+import pandas as pd
+
+from .forecast import Forecast, crps, pit
+from .models import BASELINE
+
+HORIZONS = np.array([30, 91, 182, 365, 730, 1095, 1460])
+FIRST_ORIGIN = pd.Timestamp("2014-01-01")
+ORIGIN_STEP_DAYS = 30
+COVERAGES = (0.5, 0.8, 0.95)
+
+
+def backtest(
+    models, data: pd.DataFrame, horizons=HORIZONS, score_after: pd.Timestamp | None = None
+) -> pd.DataFrame:
+    """One row per (model, origin, horizon) with an observed outcome."""
+    log_close = np.log(data["close"])
+    last = data.index[-1]
+    rows = []
+    for origin in pd.date_range(FIRST_ORIGIN, last, freq=f"{ORIGIN_STEP_DAYS}D"):
+        targets = origin + pd.to_timedelta(horizons, unit="D")
+        scored = targets <= last
+        if score_after is not None:
+            scored &= targets > score_after
+        if not scored.any():
+            continue
+        history = data.loc[:origin]
+        outcome = log_close.loc[targets[scored]].to_numpy()
+        for model in models:
+            rows.append(score(model.name, model.forecast(history, horizons[scored]), outcome))
+    return pd.concat(rows, ignore_index=True)
+
+
+def score(model: str, f: Forecast, outcome: np.ndarray) -> pd.DataFrame:
+    """Score one forecast against the observed log prices at its horizons."""
+    row = {
+        "model": model,
+        "origin": f.origin,
+        "horizon": f.horizons,
+        "outcome": outcome,
+        "median": f.quantile(0.5),
+        "crps": crps(f.log_quantiles, outcome),
+        "pit": pit(f.log_quantiles, outcome),
+    }
+    for c in COVERAGES:
+        lo, hi = f.interval(c)
+        row[f"in{c:.0%}"] = (lo <= outcome) & (outcome <= hi)
+    return pd.DataFrame(row)
+
+
+def summarize(
+    scores: pd.DataFrame,
+    baseline: str = BASELINE,
+    step_days: int = ORIGIN_STEP_DAYS,
+    n_boot: int = 2000,
+    seed: int = 0,
+) -> pd.DataFrame:
+    """
+    Per model and horizon: mean CRPS, skill relative to `baseline`, and coverage.
+
+    Skill is 1 - CRPS / baseline CRPS (positive = better than the baseline),
+    with a 90% block bootstrap interval over origins spaced `step_days` apart. Forecasts from
+    nearby origins overlap heavily, so `windows` (the span covered divided by
+    the horizon) is the honest count of independent outcomes. Treat intervals
+    with fewer than ~5 windows as optimistic.
+    """
+    rng = np.random.default_rng(seed)
+    rows = []
+    for horizon, at_h in scores.groupby("horizon"):
+        base = at_h[at_h.model == baseline].set_index("origin")["crps"].sort_index()
+        span = (base.index[-1] - base.index[0]).days + horizon
+        block = max(1, min(int(np.ceil(horizon / step_days)), len(base) // 2))
+        boot_index = _block_bootstrap_indices(len(base), block, n_boot, rng)
+        for model, g in at_h.groupby("model", sort=False):
+            m = g.set_index("origin")["crps"].reindex(base.index).to_numpy()
+            boot = 1 - m[boot_index].mean(axis=1) / base.to_numpy()[boot_index].mean(axis=1)
+            rows.append(
+                {
+                    "model": model,
+                    "horizon": horizon,
+                    "forecasts": len(g),
+                    "windows": span / horizon,
+                    "crps": g["crps"].mean(),
+                    "skill": 1 - m.mean() / base.mean(),
+                    "skill_lo": np.quantile(boot, 0.05),
+                    "skill_hi": np.quantile(boot, 0.95),
+                    **{f"cov{c:.0%}": g[f"in{c:.0%}"].mean() for c in COVERAGES},
+                    "mean_pit": g["pit"].mean(),
+                }
+            )
+    return pd.DataFrame(rows)
+
+
+def _block_bootstrap_indices(n, block, n_boot, rng) -> np.ndarray:
+    """Circular block bootstrap, so the first and last origins aren't under-sampled."""
+    n_blocks = int(np.ceil(n / block))
+    starts = rng.integers(0, n, size=(n_boot, n_blocks))
+    return ((starts[:, :, None] + np.arange(block)) % n).reshape(n_boot, -1)[:, :n]
+
+
+def format_summary(summary: pd.DataFrame, baseline: str = BASELINE) -> str:
+    table = pd.DataFrame(
+        {
+            "model": summary["model"],
+            "horizon": summary["horizon"].map(horizon_label),
+            "windows": summary["windows"].map("{:.1f}".format),
+            "crps": summary["crps"].map("{:.3f}".format),
+            f"skill vs {baseline} [90%]": [
+                f"{s:+.0%} [{lo:+.0%}, {hi:+.0%}]"
+                for s, lo, hi in zip(summary.skill, summary.skill_lo, summary.skill_hi, strict=True)
+            ],
+            **{f"in {c:.0%}": summary[f"cov{c:.0%}"].map("{:.0%}".format) for c in COVERAGES},
+            "mean pit": summary["mean_pit"].map("{:.2f}".format),
+        }
+    )
+    return table.to_string(index=False)
+
+
+def horizon_label(days: int) -> str:
+    if days < 365:
+        return f"{round(days / 30.4)}mo"
+    return f"{round(days / 365)}y"

btcmodel/experiments.py

@@ -0,0 +1,169 @@
+"""
+A/B tests of individual ideas, mostly salvaged from the 2024 model's branches.
+
+Each experiment states its hypothesis and pairs a control with variants that
+change one component. Experiments are written down before they are run, and
+every result is reported, including the failures; with a few dozen
+comparisons over a handful of independent windows, some "wins" will be luck.
+Verdicts use one rule, fixed in advance (see `verdict`), and anything that
+passes still has to hold up on the holdout.
+"""
+
+from dataclasses import dataclass
+
+import pandas as pd
+
+from .evaluate import backtest, summarize
+from .models import MODELS
+from .models.base import Composite
+from .models.drift import (
+    CycleDrift,
+    PowerLawDrift,
+    PowerLawScaledCycleDrift,
+    ShrunkDrift,
+    TrailingMeanDrift,
+)
+from .models.shape import Empirical, StudentT
+from .models.volatility import CycleVol, EwmaVol, ReversionVol, TrailingVol, TrendReversionVol
+
+
+@dataclass(frozen=True)
+class Experiment:
+    name: str
+    hypothesis: str
+    source: str  # where in the old history the idea came from
+    control: Composite
+    variants: tuple[Composite, ...]
+
+    @property
+    def models(self) -> list[Composite]:
+        return [self.control, *self.variants]
+
+
+def run(experiment: Experiment, prices: pd.DataFrame) -> tuple[pd.DataFrame, pd.DataFrame]:
+    scores = backtest(experiment.models, prices)
+    return scores, summarize(scores, baseline=experiment.control.name)
+
+
+def verdict(variant_summary: pd.DataFrame) -> str:
+    """
+    Decide from skill vs the control, per horizon, with 90% intervals:
+
+    - "worse" if the interval is entirely below zero at any horizon;
+    - "better" if the interval is entirely above zero at two or more horizons
+      and the point estimate is non-negative at every horizon;
+    - "inconclusive" otherwise.
+    """
+    if (variant_summary["skill_hi"] < 0).any():
+        return "worse"
+    if (variant_summary["skill_lo"] > 0).sum() >= 2 and (variant_summary["skill"] >= 0).all():
+        return "better"
+    return "inconclusive"
+
+
+# Idea labels (D1, V2, ...) refer to docs/2024-ideas.md.
+CYCLE = MODELS["cycle"]
+DRIFT_RW = MODELS["drift_rw"]
+POWERLAW = MODELS["powerlaw"]
+# Volatility and shape experiments use drift_rw as the control: the zero-drift
+# random walk is biased low at long horizons, so anything that merely widened
+# its intervals would look like an improvement.
+_VOL = dict(drift=TrailingMeanDrift())
+
+EXPERIMENTS: dict[str, Experiment] = {
+    e.name: e
+    for e in (
+        Experiment(
+            "shrink-cycle",
+            "the cycle drift is overfit; pulling it toward zero improves it",
+            "D2: damping constants throughout the 2024 model",
+            CYCLE,
+            tuple(
+                Composite(f"cycle_x{f}", ShrunkDrift(CycleDrift(), f), TrailingVol())
+                for f in (0.25, 0.5, 0.75)
+            ),
+        ),
+        Experiment(
+            "diminishing-returns",
+            "each cycle grows less than the last; a power-law trend captures that",
+            "D3: initial commit, old/backtests-trend-enhancement-1",
+            DRIFT_RW,
+            (
+                Composite("powerlaw", PowerLawDrift(), TrailingVol()),
+                Composite("powerlaw_revert", PowerLawDrift(revert=True), TrailingVol()),
+                Composite("cycle_on_powerlaw", PowerLawScaledCycleDrift(), TrailingVol()),
+            ),
+        ),
+        Experiment(
+            "vol-window",
+            "recent volatility predicts future volatility better than a flat 365-day window",
+            "V1: 'Add improved vol calculation'",
+            DRIFT_RW,
+            (
+                Composite("ewma_blend", volatility=EwmaVol(), **_VOL),
+                Composite("ewma_90", volatility=EwmaVol(spans=(90,), weights=(1.0,)), **_VOL),
+                Composite("trailing_730", volatility=TrailingVol(730), **_VOL),
+            ),
+        ),
+        Experiment(
+            "vol-reversion",
+            "volatility shocks fade toward a long-run level, which itself is falling",
+            "V2, V4, C2: adaptive windows, market maturity, horizon multipliers",
+            DRIFT_RW,
+            (
+                Composite("revert_level", volatility=ReversionVol(), **_VOL),
+                Composite("revert_trend", volatility=ReversionVol(long_run="trend"), **_VOL),
+            ),
+        ),
+        Experiment(
+            "cycle-vol",
+            "volatility depends on position in the halving cycle",
+            "V3: old/backtest-vol-cycle",
+            DRIFT_RW,
+            (Composite("cycle_vol", volatility=CycleVol(), **_VOL),),
+        ),
+        Experiment(
+            "tails",
+            "log returns are heavier-tailed than normal, even at long horizons",
+            "S1: skewed innovations in tuning-1",
+            DRIFT_RW,
+            (
+                Composite("student_t4", volatility=TrailingVol(), shape=StudentT(4), **_VOL),
+                Composite("empirical", volatility=TrailingVol(), shape=Empirical(), **_VOL),
+            ),
+        ),
+        Experiment(
+            "cycle-phase",
+            "cycles align better by fraction elapsed than by days since the halving",
+            "D1: the 2024 model stretched every cycle to 1460 days",
+            CYCLE,
+            (Composite("cycle_fraction", CycleDrift(phase="fraction"), TrailingVol()),),
+        ),
+        # Round 2. Before running these, the holdout candidates were fixed as:
+        # the three original models, powerlaw, and any variant below that is
+        # "better" than its control.
+        Experiment(
+            "powerlaw-ou",
+            "deviations from the power-law trend fade, so long-horizon uncertainty is bounded",
+            "follow-up to diminishing-returns: powerlaw_revert beat drift_rw, but its bands"
+            " were too wide",
+            POWERLAW,
+            (
+                Composite("powerlaw_ou", PowerLawDrift(revert=True), TrendReversionVol()),
+                Composite(
+                    "powerlaw_ou_param",
+                    PowerLawDrift(revert=True),
+                    TrendReversionVol(parameter_uncertainty=True),
+                ),
+            ),
+        ),
+        Experiment(
+            "cycle-on-powerlaw",
+            "with the level set by the power law, the cycle's timing adds information",
+            "D1 on D3. This pair was already compared informally on the same data after"
+            " round 1, so only the holdout can really settle it",
+            POWERLAW,
+            (Composite("cycle_on_powerlaw", PowerLawScaledCycleDrift(), TrailingVol()),),
+        ),
+    )
+}

btcmodel/forecast.py

@@ -0,0 +1,76 @@
+"""
+The one output format every model produces, and how it is scored.
+
+A forecast is a set of quantiles of the natural-log price at each horizon.
+Quantiles work for any model (closed-form, simulated, bootstrapped, mixtures)
+and make scoring simple. Working in log price makes errors relative: a CRPS of
+0.1 is roughly "typically 10% off", in 2013 or in 2026.
+"""
+
+from dataclasses import dataclass
+
+import numpy as np
+import pandas as pd
+from scipy.stats import norm
+
+N_LEVELS = 100
+# Midpoints of 100 equal-probability bins: 0.005, 0.015, ..., 0.995.
+LEVELS = (np.arange(N_LEVELS) + 0.5) / N_LEVELS
+
+
+@dataclass(frozen=True)
+class Forecast:
+    origin: pd.Timestamp
+    horizons: np.ndarray  # days after origin, shape (H,)
+    log_quantiles: np.ndarray  # log price at LEVELS, shape (H, N_LEVELS), rows nondecreasing
+
+    @classmethod
+    def normal(cls, origin, horizons, mean, sd) -> "Forecast":
+        """Normal distribution in log price (i.e. lognormal price) at each horizon."""
+        mean = np.broadcast_to(np.asarray(mean, dtype=float), np.shape(horizons))
+        sd = np.broadcast_to(np.asarray(sd, dtype=float), np.shape(horizons))
+        q = mean[:, None] + sd[:, None] * norm.ppf(LEVELS)[None, :]
+        return cls(pd.Timestamp(origin), np.asarray(horizons), q)
+
+    @classmethod
+    def from_samples(cls, origin, horizons, samples) -> "Forecast":
+        """Empirical quantiles of simulated log prices, shape (n_samples, H)."""
+        q = np.quantile(np.asarray(samples), LEVELS, axis=0).T
+        return cls(pd.Timestamp(origin), np.asarray(horizons), q)
+
+    @property
+    def dates(self) -> pd.DatetimeIndex:
+        return self.origin + pd.to_timedelta(self.horizons, unit="D")
+
+    def quantile(self, level: float) -> np.ndarray:
+        """Log price at an arbitrary level, interpolated between grid levels."""
+        return np.array([np.interp(level, LEVELS, row) for row in self.log_quantiles])
+
+    def interval(self, coverage: float) -> tuple[np.ndarray, np.ndarray]:
+        """Central interval in log price holding `coverage` probability."""
+        tail = (1 - coverage) / 2
+        return self.quantile(tail), self.quantile(1 - tail)
+
+
+def crps(log_quantiles: np.ndarray, outcome: np.ndarray) -> np.ndarray:
+    """
+    Continuous ranked probability score, from quantiles, in log-price units.
+
+    CRPS is twice the pinball loss integrated over all quantile levels; the
+    quantile grid gives the integral directly. It rewards sharpness and
+    calibration together and has no free parameters to game. Lower is better.
+    """
+    outcome = np.asarray(outcome, dtype=float)
+    u = outcome[..., None] - log_quantiles
+    pinball = u * (LEVELS - (u < 0))
+    return 2 * pinball.mean(axis=-1)
+
+
+def pit(log_quantiles: np.ndarray, outcome: np.ndarray) -> np.ndarray:
+    """Probability integral transform: forecast CDF evaluated at the outcome."""
+    return np.array(
+        [
+            np.interp(y, q, LEVELS, left=0.0, right=1.0)
+            for q, y in zip(np.atleast_2d(log_quantiles), np.atleast_1d(outcome), strict=True)
+        ]
+    )

btcmodel/forward.py

@@ -0,0 +1,104 @@
+"""
+Forward test: forecasts recorded before their outcomes exist.
+
+`snapshot` stores every tracked model's forecast from the latest price in
+data/forecasts/<origin>.csv. The files are committed, so version control shows
+each one was written before its outcome was known. `score_snapshots` grades
+every recorded forecast whose target date has passed, exactly as the backtest
+does.
+
+Snapshots store the forecast quantiles themselves, so model code can change
+without rewriting the record. If a model's definition changes, give it a new
+name rather than reusing the old one.
+"""
+
+import datetime as dt
+from pathlib import Path
+
+import numpy as np
+import pandas as pd
+
+from .data import DATA_DIR
+from .evaluate import HORIZONS, score
+from .experiments import EXPERIMENTS
+from .forecast import LEVELS, Forecast
+from .models import MODELS
+
+FORECASTS_DIR = DATA_DIR / "forecasts"
+# A snapshot must be made from fresh data, not reconstructed after the fact.
+MAX_DATA_AGE_DAYS = 2
+# Intended cadence (weekly), used to size bootstrap blocks when scoring.
+SNAPSHOT_STEP_DAYS = 7
+
+_VARIANTS = {m.name: m for e in EXPERIMENTS.values() for m in e.models}
+# The registered models, plus candidates that could only be settled on new data.
+TRACKED = [
+    *MODELS.values(),
+    *(_VARIANTS[n] for n in ("powerlaw_ou", "powerlaw_ou_param", "cycle_on_powerlaw")),
+]
+
+# Named by percentile: p0.5, p1.5, ..., p99.5 (the grid has no exact median).
+_QUANTILE_COLUMNS = [f"p{100 * level:.1f}" for level in LEVELS]
+
+
+def snapshot(
+    prices: pd.DataFrame,
+    models=TRACKED,
+    directory: Path = FORECASTS_DIR,
+    today: pd.Timestamp | None = None,
+) -> Path:
+    """Record each model's forecast from the last price in `prices`."""
+    origin = prices.index[-1]
+    if today is None:
+        today = pd.Timestamp(dt.datetime.now(dt.UTC).date())
+    if (today - origin).days > MAX_DATA_AGE_DAYS:
+        raise ValueError(
+            f"latest price is from {origin:%Y-%m-%d}; update the data first "
+            "(forecasts must be recorded in real time)"
+        )
+    path = directory / f"{origin:%Y-%m-%d}.csv"
+    if path.exists():
+        raise FileExistsError(f"{path} already exists")
+
+    frames = []
+    for model in models:
+        f = model.forecast(prices, HORIZONS)
+        frame = pd.DataFrame(f.log_quantiles, columns=_QUANTILE_COLUMNS)
+        frame.insert(0, "model", model.name)
+        frame.insert(1, "horizon", f.horizons)
+        frame.insert(2, "target", f.dates.strftime("%Y-%m-%d"))
+        frames.append(frame)
+    directory.mkdir(parents=True, exist_ok=True)
+    pd.concat(frames).to_csv(path, index=False, float_format="%.6f")
+    return path
+
+
+def load_snapshots(directory: Path = FORECASTS_DIR) -> list[tuple[str, Forecast]]:
+    """Every recorded forecast, as (model name, Forecast)."""
+    forecasts = []
+    for path in sorted(directory.glob("*.csv")):
+        origin = pd.Timestamp(path.stem)
+        for model, g in pd.read_csv(path).groupby("model", sort=False):
+            quantiles = g[_QUANTILE_COLUMNS].to_numpy()
+            forecasts.append((model, Forecast(origin, g["horizon"].to_numpy(), quantiles)))
+    return forecasts
+
+
+def score_snapshots(prices: pd.DataFrame, directory: Path = FORECASTS_DIR) -> pd.DataFrame:
+    """Score every recorded forecast horizon whose target date is in `prices`."""
+    log_close = np.log(prices["close"])
+    rows = []
+    for model, f in load_snapshots(directory):
+        due = f.dates <= prices.index[-1]
+        if not due.any():
+            continue
+        due_forecast = Forecast(f.origin, f.horizons[due], f.log_quantiles[due])
+        outcome = log_close.loc[due_forecast.dates].to_numpy()
+        rows.append(score(model, due_forecast, outcome))
+    return pd.concat(rows, ignore_index=True) if rows else pd.DataFrame()
+
+
+def next_due(prices: pd.DataFrame, directory: Path = FORECASTS_DIR) -> pd.Timestamp | None:
+    """The earliest target date not yet observed, if any."""
+    pending = [d for _, f in load_snapshots(directory) for d in f.dates if d > prices.index[-1]]
+    return min(pending) if pending else None

btcmodel/halving.py

@@ -0,0 +1,41 @@
+"""Halving calendar and position within the halving cycle."""
+
+import numpy as np
+import pandas as pd
+
+GENESIS = pd.Timestamp("2009-01-03")
+
+# Block heights 210k, 420k, 630k, 840k (UTC dates).
+HALVINGS = pd.DatetimeIndex(["2012-11-28", "2016-07-09", "2020-05-11", "2024-04-20"])
+
+# Later halvings are projected at the length of the last cycle. Block times drift
+# by weeks per cycle, which is noise at the resolution this is used.
+_LAST_CYCLE = HALVINGS[-1] - HALVINGS[-2]
+_PROJECTED = pd.DatetimeIndex([HALVINGS[-1] + k * _LAST_CYCLE for k in range(1, 6)])
+
+# Genesis starts cycle 0.
+CYCLE_STARTS = pd.DatetimeIndex([GENESIS]).append(HALVINGS).append(_PROJECTED)
+
+
+def cycle_position(dates) -> tuple[np.ndarray, np.ndarray]:
+    """
+    For each date, return (cycle index, days since that cycle began).
+
+    Cycle 0 runs from genesis to the first halving; a halving day is day 0 of
+    the cycle it starts.
+    """
+    dates = pd.DatetimeIndex(dates)
+    if (dates < GENESIS).any():
+        raise ValueError("date before genesis")
+    if (dates >= CYCLE_STARTS[-1]).any():
+        raise ValueError("date beyond projected halvings")
+    index = CYCLE_STARTS.searchsorted(dates, side="right") - 1
+    days = (dates - CYCLE_STARTS[index]).days
+    return np.asarray(index), np.asarray(days)
+
+
+def cycle_fraction(dates) -> tuple[np.ndarray, np.ndarray]:
+    """For each date, return (cycle index, fraction of that cycle elapsed, in [0, 1))."""
+    index, days = cycle_position(dates)
+    lengths = (CYCLE_STARTS[index + 1] - CYCLE_STARTS[index]).days
+    return index, days / np.asarray(lengths)

btcmodel/models/__init__.py

@@ -0,0 +1,30 @@
+"""
+Candidate models.
+
+A model is any object with a `name` and a
+`forecast(history: pd.DataFrame, horizons: np.ndarray) -> Forecast` method.
+`history` holds every row up to and including the forecast origin and nothing
+after it; the harness guarantees that, so models can use all of it freely.
+Most models are a Composite of a drift and a volatility component.
+"""
+
+from .base import Composite
+from .drift import CycleDrift, PowerLawDrift, TrailingMeanDrift, ZeroDrift
+from .volatility import TrailingVol
+
+BASELINE = "random_walk"
+
+# Order is fixed: it sets each model's colour in every chart.
+MODELS = {
+    m.name: m
+    for m in (
+        # "It stays about here, give or take."
+        Composite(BASELINE, ZeroDrift(), TrailingVol()),
+        # "It keeps doing what it did last cycle."
+        Composite("drift_rw", TrailingMeanDrift(), TrailingVol()),
+        # The 2024 model, distilled.
+        Composite("cycle", CycleDrift(), TrailingVol()),
+        # "Growth keeps slowing, like it always has." Passed the diminishing-returns A/B.
+        Composite("powerlaw", PowerLawDrift(), TrailingVol()),
+    )
+}

btcmodel/models/base.py

@@ -0,0 +1,50 @@
+"""
+Models built from parts.
+
+Most ideas about Bitcoin prices say something about either the expected return
+(drift) or the size of the uncertainty (volatility). A Composite pairs one of
+each, so an A/B test can swap exactly one part and hold the other fixed.
+"""
+
+from dataclasses import dataclass
+from typing import Protocol
+
+import numpy as np
+import pandas as pd
+
+from ..forecast import Forecast
+from .shape import Normal
+
+
+class Drift(Protocol):
+    def expected_log_return(self, history: pd.DataFrame, horizons: np.ndarray) -> np.ndarray:
+        """Expected cumulative log return from the origin to each horizon."""
+        ...
+
+
+class Volatility(Protocol):
+    def sd(self, history: pd.DataFrame, horizons: np.ndarray) -> np.ndarray:
+        """Standard deviation of the cumulative log return at each horizon."""
+        ...
+
+
+class Shape(Protocol):
+    def standard_quantiles(self, history: pd.DataFrame, horizons: np.ndarray) -> np.ndarray:
+        """Quantiles at LEVELS of a mean-0, sd-1 distribution, shape (H, N_LEVELS)."""
+        ...
+
+
+@dataclass(frozen=True)
+class Composite:
+    """Log price: mean from `drift`, spread from `volatility`, normal unless `shape` says."""
+
+    name: str
+    drift: Drift
+    volatility: Volatility
+    shape: Shape = Normal()
+
+    def forecast(self, history: pd.DataFrame, horizons: np.ndarray) -> Forecast:
+        mean = np.log(history["close"].iloc[-1]) + self.drift.expected_log_return(history, horizons)
+        sd = self.volatility.sd(history, horizons)
+        z = self.shape.standard_quantiles(history, horizons)
+        return Forecast(history.index[-1], horizons, mean[:, None] + sd[:, None] * z)

btcmodel/models/drift.py

@@ -0,0 +1,175 @@
+"""Expected-return components."""
+
+from dataclasses import dataclass
+
+import numpy as np
+import pandas as pd
+
+from ..data import log_returns
+from ..halving import GENESIS, cycle_fraction, cycle_position
+
+# Longer than any cycle so far (the longest, cycle 0, is 1425 days).
+MAX_CYCLE_DAYS = 1500
+# Length every cycle is stretched to when phase="fraction".
+NOMINAL_CYCLE_DAYS = 1440
+
+
+def mean_by_cycle_day(values, day, weight, bandwidth_days, prior_days) -> np.ndarray:
+    """
+    Weighted mean of `values` around each day of the cycle, shape (MAX_CYCLE_DAYS,).
+
+    Neighbouring days are pooled with a Gaussian kernel. Where the data is thin,
+    the mean shrinks toward the overall weighted mean, as if `prior_days` extra
+    observations sat at that value.
+    """
+    sum_wv = np.bincount(day, weights=weight * values, minlength=MAX_CYCLE_DAYS)
+    sum_w = np.bincount(day, weights=weight, minlength=MAX_CYCLE_DAYS)
+
+    # Peak-1 kernel, so smoothed weights count (weighted) days of data.
+    half_width = int(np.ceil(4 * bandwidth_days))
+    offsets = np.arange(-half_width, half_width + 1)
+    kernel = np.exp(-0.5 * (offsets / bandwidth_days) ** 2)
+    smooth_wv = np.convolve(sum_wv, kernel, mode="same")
+    smooth_w = np.convolve(sum_w, kernel, mode="same")
+
+    overall = sum_wv.sum() / sum_w.sum()
+    return (smooth_wv + prior_days * overall) / (smooth_w + prior_days)
+
+
+@dataclass(frozen=True)
+class ZeroDrift:
+    """No expected change in log price."""
+
+    def expected_log_return(self, history: pd.DataFrame, horizons: np.ndarray) -> np.ndarray:
+        return np.zeros(len(horizons))
+
+
+@dataclass(frozen=True)
+class TrailingMeanDrift:
+    """Mean daily log return over the trailing `window` days, extrapolated."""
+
+    window: int = 1460
+
+    def expected_log_return(self, history: pd.DataFrame, horizons: np.ndarray) -> np.ndarray:
+        return log_returns(history).iloc[-self.window :].mean() * horizons
+
+
+@dataclass(frozen=True)
+class CycleDrift:
+    """
+    Expected return depends on how many days it has been since the last halving.
+
+    The drift for day d of the cycle is a weighted mean of the daily log returns
+    observed around day d of every past cycle. Of the 2024 model's ~2000 lines,
+    this idea did all the work. It differs from that model in two ways:
+
+    - Neighbouring cycle days are pooled with a Gaussian kernel. The 2024 model
+      averaged each day separately and then took a rolling mean.
+    - Past cycles are down-weighted, halving each `recency_half_life` cycles, so
+      the 10-100x cycles of 2011-2017 don't set the level. The 2024 model
+      averaged all cycles equally, then scaled by ~0.7; it overshot the
+      2025 peak by ~60%. (This is the idea on the old `tuning-b` branch.)
+
+    Where the data is thin, the drift shrinks toward the overall mean (see
+    `mean_by_cycle_day`).
+
+    `phase="days"` aligns cycles by days since the halving; `phase="fraction"`
+    stretches every cycle to NOMINAL_CYCLE_DAYS, as the 2024 model did.
+    """
+
+    bandwidth_days: float = 30.0
+    recency_half_life: float = 1.0
+    prior_days: float = 10.0
+    phase: str = "days"
+
+    def position(self, dates) -> tuple[np.ndarray, np.ndarray]:
+        """(cycle index, cycle day) under this model's phase convention."""
+        if self.phase == "days":
+            return cycle_position(dates)
+        if self.phase == "fraction":
+            index, fraction = cycle_fraction(dates)
+            return index, np.round(fraction * NOMINAL_CYCLE_DAYS).astype(int)
+        raise ValueError(f"unknown phase {self.phase!r}")
+
+    def by_cycle_day(self, history: pd.DataFrame) -> np.ndarray:
+        """Expected daily log return for each day of the cycle, shape (MAX_CYCLE_DAYS,)."""
+        returns = log_returns(history)
+        cycle, day = self.position(returns.index)
+        current_cycle = self.position(history.index[-1:])[0][0]
+        return mean_by_cycle_day(
+            returns.to_numpy(),
+            day,
+            weight=0.5 ** ((current_cycle - cycle) / self.recency_half_life),
+            bandwidth_days=self.bandwidth_days,
+            prior_days=self.prior_days,
+        )
+
+    def expected_log_return(self, history: pd.DataFrame, horizons: np.ndarray) -> np.ndarray:
+        drift = self.by_cycle_day(history)
+        future = history.index[-1] + pd.to_timedelta(np.arange(1, horizons.max() + 1), unit="D")
+        _, future_day = self.position(future)
+        return np.cumsum(drift[future_day])[horizons - 1]
+
+
+@dataclass(frozen=True)
+class ShrunkDrift:
+    """Another drift scaled by `factor`: 0 is no drift, 1 is the original."""
+
+    inner: CycleDrift | TrailingMeanDrift
+    factor: float
+
+    def expected_log_return(self, history: pd.DataFrame, horizons: np.ndarray) -> np.ndarray:
+        return self.factor * self.inner.expected_log_return(history, horizons)
+
+
+@dataclass(frozen=True)
+class PowerLawDrift:
+    """
+    Log price grows linearly in log time since genesis: ln P = a + b ln t.
+
+    Growth therefore slows like b/t, which is the diminishing returns the
+    cycle-by-cycle numbers show. The line is fitted by least squares to the
+    history. With `revert=True` the gap between price and line also closes,
+    at the rate of an AR(1) fitted to the daily residuals.
+    """
+
+    revert: bool = False
+
+    def fit(self, history: pd.DataFrame) -> tuple[float, float, float]:
+        """Return (intercept, slope, daily AR(1) coefficient of the residuals)."""
+        log_t = np.log((history.index - GENESIS).days.to_numpy())
+        log_p = np.log(history["close"].to_numpy())
+        slope, intercept = np.polyfit(log_t, log_p, 1)
+        resid = log_p - (intercept + slope * log_t)
+        phi = resid[1:] @ resid[:-1] / (resid[:-1] @ resid[:-1])
+        return intercept, slope, phi
+
+    def expected_log_return(self, history: pd.DataFrame, horizons: np.ndarray) -> np.ndarray:
+        intercept, slope, phi = self.fit(history)
+        t0 = (history.index[-1] - GENESIS).days
+        trend = slope * np.log((t0 + horizons) / t0)
+        if not self.revert:
+            return trend
+        gap = np.log(history["close"].iloc[-1]) - (intercept + slope * np.log(t0))
+        return trend + (phi**horizons - 1) * gap
+
+
+@dataclass(frozen=True)
+class PowerLawScaledCycleDrift:
+    """
+    The cycle shape, rescaled so its average over a cycle equals the power-law
+    trend's growth rate over the next cycle: keep the timing, fix the level.
+    """
+
+    cycle: CycleDrift = CycleDrift()
+
+    def expected_log_return(self, history: pd.DataFrame, horizons: np.ndarray) -> np.ndarray:
+        shape = self.cycle.by_cycle_day(history)
+        cycle_mean = shape[:NOMINAL_CYCLE_DAYS].mean()
+        level = PowerLawDrift().expected_log_return(history, np.array([NOMINAL_CYCLE_DAYS]))[0]
+        level /= NOMINAL_CYCLE_DAYS
+        if cycle_mean <= 1e-6:
+            return level * horizons
+        future = history.index[-1] + pd.to_timedelta(np.arange(1, horizons.max() + 1), unit="D")
+        _, future_day = self.cycle.position(future)
+        return np.cumsum(shape[future_day] * level / cycle_mean)[horizons - 1]

btcmodel/models/shape.py

@@ -0,0 +1,52 @@
+"""Distribution shapes: standardised quantiles (mean 0, sd 1) at each horizon."""
+
+from dataclasses import dataclass
+
+import numpy as np
+import pandas as pd
+from scipy.stats import norm, t
+
+from ..forecast import LEVELS
+
+
+@dataclass(frozen=True)
+class Normal:
+    def standard_quantiles(self, history: pd.DataFrame, horizons: np.ndarray) -> np.ndarray:
+        return np.broadcast_to(norm.ppf(LEVELS), (len(horizons), len(LEVELS)))
+
+
+@dataclass(frozen=True)
+class StudentT:
+    """Student's t with `df` degrees of freedom, rescaled to unit variance."""
+
+    df: float = 4.0
+
+    def standard_quantiles(self, history: pd.DataFrame, horizons: np.ndarray) -> np.ndarray:
+        q = t.ppf(LEVELS, self.df) / np.sqrt(self.df / (self.df - 2))
+        return np.broadcast_to(q, (len(horizons), len(LEVELS)))
+
+
+@dataclass(frozen=True)
+class Empirical:
+    """
+    Filtered historical simulation at the horizon level: the shape of past
+    h-day log returns, each divided by the trailing volatility at its start.
+
+    Overlapping h-day returns are far from independent, so a horizon falls back
+    to normal unless the history spans at least `min_windows` of them.
+    """
+
+    vol_window: int = 365
+    min_windows: int = 3
+
+    def standard_quantiles(self, history: pd.DataFrame, horizons: np.ndarray) -> np.ndarray:
+        log_price = np.log(history["close"])
+        sigma = log_price.diff().rolling(self.vol_window).std()
+        out = np.empty((len(horizons), len(LEVELS)))
+        for i, h in enumerate(horizons):
+            z = ((log_price.shift(-h) - log_price) / (sigma * np.sqrt(h))).dropna()
+            if len(z) < self.min_windows * h:
+                out[i] = norm.ppf(LEVELS)
+            else:
+                out[i] = np.quantile((z - z.mean()) / z.std(), LEVELS)
+        return out

btcmodel/models/volatility.py

@@ -0,0 +1,146 @@
+"""Uncertainty components."""
+
+from dataclasses import dataclass
+
+import numpy as np
+import pandas as pd
+
+from ..data import log_returns
+from ..halving import GENESIS, cycle_position
+from .drift import PowerLawDrift, mean_by_cycle_day
+
+
+@dataclass(frozen=True)
+class TrailingVol:
+    """Standard deviation of daily log returns over the trailing `window` days, scaled by √h."""
+
+    window: int = 365
+
+    def sd(self, history: pd.DataFrame, horizons: np.ndarray) -> np.ndarray:
+        return log_returns(history).iloc[-self.window :].std() * np.sqrt(horizons)
+
+
+@dataclass(frozen=True)
+class EwmaVol:
+    """Weighted blend of exponentially weighted standard deviations, scaled by √h."""
+
+    spans: tuple[int, ...] = (30, 90, 180)
+    weights: tuple[float, ...] = (0.2, 0.5, 0.3)
+
+    def sd(self, history: pd.DataFrame, horizons: np.ndarray) -> np.ndarray:
+        returns = log_returns(history)
+        sigma = sum(
+            w * returns.ewm(span=s).std().iloc[-1]
+            for s, w in zip(self.spans, self.weights, strict=True)
+        )
+        return sigma * np.sqrt(horizons)
+
+
+@dataclass(frozen=True)
+class ReversionVol:
+    """
+    Volatility starts at its current (short EWMA) level and decays toward a
+    long-run level with a `half_life_days` half-life.
+
+    `long_run="level"` uses the trailing `long_window` standard deviation;
+    `long_run="trend"` extrapolates a log-linear trend in 90-day realised
+    volatility over the same window, since volatility has fallen for years.
+    """
+
+    now_span: int = 30
+    half_life_days: float = 90.0
+    long_run: str = "level"
+    long_window: int = 1460
+
+    def sd(self, history: pd.DataFrame, horizons: np.ndarray) -> np.ndarray:
+        returns = log_returns(history)
+        now = returns.ewm(span=self.now_span).std().iloc[-1]
+        days = np.arange(1, horizons.max() + 1)
+        trailing = returns.iloc[-self.long_window :]
+        if self.long_run == "level":
+            long_run = np.full(len(days), trailing.std())
+        elif self.long_run == "trend":
+            # Non-overlapping 90-day windows, anchored at the origin.
+            realised = trailing.rolling(90).std().iloc[::-90].dropna()
+            age = (realised.index - history.index[-1]).days.to_numpy()
+            slope, intercept = np.polyfit(age, np.log(realised.to_numpy()), 1)
+            long_run = np.exp(intercept + slope * days)
+        else:
+            raise ValueError(f"unknown long_run {self.long_run!r}")
+        phi = 0.5 ** (1 / self.half_life_days)
+        daily_var = long_run**2 + (now**2 - long_run**2) * phi**days
+        return np.sqrt(np.cumsum(daily_var)[horizons - 1])
+
+
+@dataclass(frozen=True)
+class CycleVol:
+    """
+    Trailing volatility, modulated by how volatile each day of the halving
+    cycle has been relative to the rest of the cycle.
+
+    The per-day ratio is estimated like CycleDrift's drift (kernel-smoothed,
+    recency-weighted), then pulled `shrink` of the way back toward 1. The
+    trailing estimate is first divided by the ratio it was measured under, so
+    the cycle effect isn't counted twice.
+    """
+
+    window: int = 365
+    bandwidth_days: float = 30.0
+    recency_half_life: float = 1.0
+    shrink: float = 0.5
+
+    def sd(self, history: pd.DataFrame, horizons: np.ndarray) -> np.ndarray:
+        returns = log_returns(history)
+        cycle, day = cycle_position(returns.index)
+        current_cycle = cycle_position(history.index[-1:])[0][0]
+        weight = 0.5 ** ((current_cycle - cycle) / self.recency_half_life)
+        squared = returns.to_numpy() ** 2
+        variance = mean_by_cycle_day(squared, day, weight, self.bandwidth_days, prior_days=10.0)
+        overall = (weight * squared).sum() / weight.sum()
+        ratio = 1 + (1 - self.shrink) * (np.sqrt(variance / overall) - 1)
+
+        past_ratio = ratio[day[-self.window :]]
+        base = returns.iloc[-self.window :].std() / np.sqrt(np.mean(past_ratio**2))
+        future = history.index[-1] + pd.to_timedelta(np.arange(1, horizons.max() + 1), unit="D")
+        _, future_day = cycle_position(future)
+        return base * np.sqrt(np.cumsum(ratio[future_day] ** 2)[horizons - 1])
+
+
+@dataclass(frozen=True)
+class TrendReversionVol:
+    """
+    Uncertainty for a price that reverts to the power-law trend.
+
+    Deviations from the trend follow a daily AR(1) with coefficient φ (fitted
+    by PowerLawDrift), so their variance levels off: after h days it is
+    σ²(1 − φ^2h) / (1 − φ²), with σ the trailing `window`-day volatility.
+
+    With `parameter_uncertainty`, the uncertainty of the fitted trend line is
+    added. The residuals are so autocorrelated that ~5000 days carry the
+    information of only n(1 − φ)/(1 + φ) independent points, and the
+    coefficient covariance is inflated to match.
+    """
+
+    window: int = 365
+    parameter_uncertainty: bool = False
+
+    def sd(self, history: pd.DataFrame, horizons: np.ndarray) -> np.ndarray:
+        intercept, slope, phi = PowerLawDrift().fit(history)
+        phi = min(phi, 0.9999)
+        sigma = log_returns(history).iloc[-self.window :].std()
+        variance = sigma**2 * (1 - phi ** (2 * horizons)) / (1 - phi**2)
+        if self.parameter_uncertainty:
+            variance = variance + self._trend_variance(history, horizons, intercept, slope, phi)
+        return np.sqrt(variance)
+
+    @staticmethod
+    def _trend_variance(history, horizons, intercept, slope, phi) -> np.ndarray:
+        t = (history.index - GENESIS).days.to_numpy()
+        x = np.column_stack([np.ones(len(t)), np.log(t)])
+        resid = np.log(history["close"].to_numpy()) - x @ [intercept, slope]
+        n_eff = len(t) * (1 - phi) / (1 + phi)
+        cov = resid.var() * np.linalg.inv(x.T @ x) * len(t) / n_eff
+        # The forecast mean is a(1 − φ^h) + b(ln t_h − φ^h ln t_0) + φ^h ln P_0.
+        decay = phi**horizons
+        g = np.column_stack([1 - decay, np.log(t[-1] + horizons) - decay * np.log(t[-1])])
+        return np.einsum("hi,ij,hj->h", g, cov, g)

btcmodel/plots.py

@@ -0,0 +1,179 @@
+"""Charts. One colour per model, fixed by its position in MODELS."""
+
+from pathlib import Path
+
+import matplotlib
+
+matplotlib.use("Agg")
+
+import matplotlib.pyplot as plt  # noqa: E402
+import numpy as np  # noqa: E402
+import pandas as pd  # noqa: E402
+from matplotlib.ticker import FuncFormatter, LogLocator, PercentFormatter  # noqa: E402
+
+from .evaluate import COVERAGES, horizon_label  # noqa: E402
+from .forecast import Forecast  # noqa: E402
+from .halving import CYCLE_STARTS  # noqa: E402
+from .models import BASELINE, MODELS  # noqa: E402
+
+SURFACE = "#fcfcfb"
+INK = "#0b0b0b"
+INK_SECONDARY = "#52514e"
+MUTED = "#898781"
+GRID = "#e1e0d9"
+AXIS = "#c3c2b7"
+SERIES = ["#2a78d6", "#eb6834", "#1baf7a", "#eda100", "#e87ba4", "#008300", "#4a3aa7", "#e34948"]
+
+plt.rcParams.update(
+    {
+        "figure.facecolor": SURFACE,
+        "axes.facecolor": SURFACE,
+        "savefig.facecolor": SURFACE,
+        "axes.edgecolor": AXIS,
+        "axes.linewidth": 0.8,
+        "axes.labelcolor": INK_SECONDARY,
+        "axes.titlecolor": INK,
+        "axes.titlesize": 11,
+        "axes.titleweight": "semibold",
+        "axes.titlelocation": "left",
+        "axes.spines.top": False,
+        "axes.spines.right": False,
+        "axes.grid": True,
+        "grid.color": GRID,
+        "grid.linewidth": 0.8,
+        "xtick.color": MUTED,
+        "ytick.color": MUTED,
+        "xtick.labelcolor": INK_SECONDARY,
+        "ytick.labelcolor": INK_SECONDARY,
+        "legend.frameon": False,
+        "legend.labelcolor": INK_SECONDARY,
+        "lines.linewidth": 2,
+        "lines.solid_capstyle": "round",
+        "lines.solid_joinstyle": "round",
+        "font.family": "sans-serif",
+        "font.size": 9,
+    }
+)
+
+
+def model_colors(names) -> dict[str, str]:
+    """Registered models keep their MODELS slot; others follow in order of appearance."""
+    names = list(dict.fromkeys(names))
+    if all(n in MODELS for n in names):
+        return {n: SERIES[list(MODELS).index(n)] for n in names}
+    return {n: SERIES[i % len(SERIES)] for i, n in enumerate(names)}
+
+
+def price_formatter(x, _=None) -> str:
+    for scale, suffix in ((1e9, "B"), (1e6, "M"), (1e3, "K")):
+        if x >= scale:
+            return f"${x / scale:.3g}{suffix}"
+    return f"${x:.3g}"
+
+
+def fan_chart(history: pd.DataFrame, forecasts: dict[str, Forecast], path: Path) -> None:
+    """History plus 50/80/95% intervals, one panel per model on shared axes."""
+    fig, axes = plt.subplots(
+        len(forecasts), 1, figsize=(10, 3.2 * len(forecasts)), sharex=True, sharey=True
+    )
+    axes = np.atleast_1d(axes)
+    shown = history[history.index >= history.index[-1] - pd.Timedelta(days=6 * 365)]
+    colors = model_colors(forecasts)
+    for ax, (name, f) in zip(axes, forecasts.items(), strict=True):
+        color = colors[name]
+        for c in sorted(COVERAGES, reverse=True):
+            lo, hi = f.interval(c)
+            ax.fill_between(f.dates, np.exp(lo), np.exp(hi), color=color, alpha=0.1, lw=0)
+        median = np.exp(f.quantile(0.5))
+        ax.plot(shown.index, shown["close"], color=INK, lw=1.2)
+        ax.plot(f.dates, median, color=color)
+        ax.annotate(
+            f"median {price_formatter(median[-1])}",
+            (f.dates[-1], median[-1]),
+            xytext=(6, 0),
+            textcoords="offset points",
+            va="center",
+            color=INK_SECONDARY,
+        )
+        for start in CYCLE_STARTS:
+            if shown.index[0] <= start <= f.dates[-1]:
+                ax.axvline(start, color=AXIS, lw=0.8, zorder=0)
+        ax.set_yscale("log")
+        ax.yaxis.set_major_locator(LogLocator(base=10, subs=(1, 2, 5)))
+        ax.yaxis.set_major_formatter(FuncFormatter(price_formatter))
+        ax.yaxis.set_minor_formatter(FuncFormatter(lambda *_: ""))
+        ax.set_title(f"{name}: forecast from {f.origin:%Y-%m-%d}")
+    axes[0].fill_between([], [], color=MUTED, alpha=0.3, label="50% interval")
+    axes[0].fill_between([], [], color=MUTED, alpha=0.2, label="80% interval")
+    axes[0].fill_between([], [], color=MUTED, alpha=0.1, label="95% interval")
+    axes[0].legend(loc="upper left")
+    axes[-1].set_xlabel("vertical lines: halvings (future ones projected)", color=MUTED)
+    fig.tight_layout()
+    fig.savefig(path, dpi=150)
+    plt.close(fig)
+
+
+def skill_chart(summary: pd.DataFrame, path: Path, title: str, baseline: str = BASELINE) -> None:
+    """CRPS skill vs `baseline`, by horizon, with bootstrap intervals."""
+    horizons = sorted(summary["horizon"].unique())
+    x = np.arange(len(horizons))
+    colors = model_colors(summary["model"])
+    fig, ax = plt.subplots(figsize=(8, 4.5))
+    ax.axhline(0, color=colors[baseline], lw=2, label=baseline)
+    for name, g in summary[summary.model != baseline].groupby("model", sort=False):
+        g = g.set_index("horizon").reindex(horizons)
+        color = colors[name]
+        ax.fill_between(x, g.skill_lo, g.skill_hi, color=color, alpha=0.1, lw=0)
+        ax.plot(x, g.skill, color=color, marker="o", ms=6, mec=SURFACE, mew=2, label=name)
+        ax.annotate(
+            name,
+            (x[-1], g.skill.iloc[-1]),
+            xytext=(8, 0),
+            textcoords="offset points",
+            va="center",
+            color=INK_SECONDARY,
+        )
+    ax.set_xticks(x, [horizon_label(h) for h in horizons])
+    ax.set_xlabel("forecast horizon")
+    ax.set_ylabel(f"CRPS skill vs {baseline} (higher is better)")
+    ax.yaxis.set_major_formatter(PercentFormatter(1.0, decimals=0))
+    ax.set_title(title)
+    ax.legend(loc="lower left")
+    fig.tight_layout()
+    fig.savefig(path, dpi=150)
+    plt.close(fig)
+
+
+def calibration_chart(summary: pd.DataFrame, path: Path, title: str) -> None:
+    """How often each nominal interval contained the outcome, by horizon."""
+    horizons = sorted(summary["horizon"].unique())
+    x = np.arange(len(horizons))
+    colors = model_colors(summary["model"])
+    fig, axes = plt.subplots(1, len(COVERAGES), figsize=(12, 4), sharey=True)
+    for ax, c in zip(axes, COVERAGES, strict=True):
+        ax.axhline(c, color=INK_SECONDARY, lw=1)
+        ax.annotate(
+            "target", (x[-1], c), xytext=(0, 4), textcoords="offset points", ha="right", color=MUTED
+        )
+        for name, g in summary.groupby("model", sort=False):
+            g = g.set_index("horizon").reindex(horizons)
+            ax.plot(
+                x,
+                g[f"cov{c:.0%}"],
+                color=colors[name],
+                marker="o",
+                ms=6,
+                mec=SURFACE,
+                mew=2,
+                label=name,
+            )
+        ax.set_xticks(x, [horizon_label(h) for h in horizons])
+        ax.set_title(f"{c:.0%} interval")
+        ax.set_ylim(0, 1.02)
+        ax.yaxis.set_major_formatter(PercentFormatter(1.0, decimals=0))
+    axes[0].set_ylabel("share of outcomes inside")
+    axes[-1].legend(loc="lower left")
+    fig.suptitle(title, x=0.01, ha="left", color=INK, fontsize=11, fontweight="semibold")
+    fig.tight_layout()
+    fig.savefig(path, dpi=150)
+    plt.close(fig)

data/coinbase.csv

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+powerlaw_ou_param,730,2028-09-22,11.120857,11.310984,11.409448,11.478825,11.533423,11.578972,11.618377,11.653320,11.684870,11.713747,11.740463,11.765396,11.788830,11.810988,11.832047,11.852150,11.871413,11.889934,11.907795,11.925065,11.941805,11.958066,11.973894,11.989328,12.004402,12.019150,12.033597,12.047770,12.061692,12.075382,12.088860,12.102143,12.115247,12.128187,12.140976,12.153628,12.166154,12.178565,12.190872,12.203086,12.215215,12.227270,12.239258,12.251188,12.263069,12.274908,12.286714,12.298494,12.310255,12.322004,12.333751,12.345501,12.357262,12.369041,12.380847,12.392686,12.404567,12.416498,12.428486,12.440540,12.452669,12.464883,12.477190,12.489602,12.502127,12.514779,12.527568,12.540508,12.553612,12.566895,12.580373,12.594064,12.607985,12.622158,12.636606,12.651353,12.666428,12.681861,12.697689,12.713950,12.730690,12.747961,12.765821,12.784342,12.803606,12.823708,12.844767,12.866926,12.890360,12.915292,12.942008,12.970885,13.002435,13.037378,13.076783,13.122332,13.176930,13.246307,13.344771,13.534898
+powerlaw_ou_param,1095,2029-09-22,11.337474,11.540910,11.646266,11.720499,11.778919,11.827657,11.869820,11.907209,11.940967,11.971865,12.000452,12.027129,12.052204,12.075913,12.098446,12.119956,12.140568,12.160385,12.179496,12.197976,12.215887,12.233287,12.250222,12.266736,12.282866,12.298646,12.314105,12.329270,12.344166,12.358814,12.373236,12.387448,12.401470,12.415315,12.429000,12.442537,12.455940,12.469220,12.482389,12.495457,12.508436,12.521334,12.534161,12.546927,12.559639,12.572307,12.584939,12.597543,12.610128,12.622700,12.635269,12.647841,12.660425,12.673029,12.685661,12.698330,12.711042,12.723808,12.736635,12.749533,12.762512,12.775580,12.788749,12.802029,12.815432,12.828969,12.842653,12.856499,12.870520,12.884733,12.899155,12.913803,12.928699,12.943864,12.959323,12.975103,12.991233,13.007747,13.024682,13.042081,13.059993,13.078473,13.097584,13.117401,13.138013,13.159522,13.182056,13.205765,13.230840,13.257517,13.286104,13.317002,13.350760,13.388149,13.430312,13.479050,13.537469,13.611703,13.717059,13.920495
+powerlaw_ou_param,1460,2030-09-22,11.556555,11.767714,11.877071,11.954123,12.014760,12.065348,12.109112,12.147921,12.182960,12.215032,12.244703,12.272394,12.298420,12.323030,12.346419,12.368745,12.390139,12.410709,12.430546,12.449727,12.468318,12.486378,12.503957,12.521098,12.537840,12.554219,12.570265,12.586006,12.601467,12.616672,12.631641,12.646393,12.660947,12.675318,12.689522,12.703573,12.717485,12.731269,12.744938,12.758503,12.771974,12.785362,12.798676,12.811926,12.825121,12.838270,12.851382,12.864465,12.877527,12.890576,12.903622,12.916672,12.929734,12.942816,12.955928,12.969077,12.982272,12.995522,13.008837,13.022225,13.035696,13.049260,13.062929,13.076714,13.090625,13.104676,13.118880,13.133252,13.147805,13.162558,13.177527,13.192731,13.208193,13.223934,13.239979,13.256358,13.273100,13.290241,13.307820,13.325880,13.344472,13.363653,13.383489,13.404059,13.425453,13.447780,13.471168,13.495778,13.521804,13.549495,13.579167,13.611238,13.646278,13.685086,13.728850,13.779439,13.840076,13.917127,14.026484,14.237643
+cycle_on_powerlaw,30,2026-10-23,11.013061,11.065946,11.093335,11.112633,11.127820,11.140490,11.151451,11.161171,11.169946,11.177979,11.185410,11.192345,11.198864,11.205027,11.210885,11.216477,11.221835,11.226987,11.231955,11.236759,11.241416,11.245939,11.250341,11.254634,11.258828,11.262930,11.266948,11.270891,11.274763,11.278571,11.282320,11.286015,11.289660,11.293259,11.296817,11.300336,11.303820,11.307273,11.310696,11.314093,11.317467,11.320820,11.324155,11.327473,11.330778,11.334071,11.337355,11.340632,11.343903,11.347172,11.350439,11.353707,11.356979,11.360256,11.363539,11.366833,11.370137,11.373456,11.376791,11.380144,11.383518,11.386915,11.390338,11.393791,11.397275,11.400794,11.404351,11.407951,11.411596,11.415291,11.419040,11.422848,11.426720,11.430662,11.434681,11.438783,11.442977,11.447270,11.451672,11.456195,11.460852,11.465656,11.470624,11.475776,11.481134,11.486726,11.492583,11.498747,11.505265,11.512201,11.519632,11.527664,11.536440,11.546160,11.557121,11.569791,11.584978,11.604276,11.631665,11.684550
+cycle_on_powerlaw,91,2026-12-23,10.794570,10.886678,10.934380,10.967990,10.994440,11.016507,11.035597,11.052525,11.067809,11.081799,11.094742,11.106821,11.118173,11.128908,11.139110,11.148849,11.158181,11.167154,11.175807,11.184174,11.192283,11.200161,11.207829,11.215306,11.222609,11.229753,11.236753,11.243619,11.250363,11.256996,11.263525,11.269960,11.276308,11.282577,11.288773,11.294902,11.300970,11.306983,11.312946,11.318863,11.324739,11.330579,11.336386,11.342166,11.347922,11.353657,11.359377,11.365083,11.370781,11.376474,11.382164,11.387856,11.393554,11.399261,11.404980,11.410716,11.416472,11.422251,11.428059,11.433899,11.439775,11.445692,11.451654,11.457667,11.463735,11.469864,11.476060,11.482329,11.488677,11.495113,11.501642,11.508274,11.515019,11.521885,11.528884,11.536028,11.543332,11.550808,11.558476,11.566354,11.574464,11.582831,11.591484,11.600456,11.609788,11.619527,11.629729,11.640464,11.651817,11.663896,11.676838,11.690828,11.706112,11.723041,11.742131,11.764198,11.790648,11.824258,11.871959,11.964068
+cycle_on_powerlaw,182,2027-03-24,10.727596,10.857857,10.925317,10.972849,11.010255,11.041463,11.068460,11.092400,11.114016,11.133800,11.152104,11.169186,11.185241,11.200422,11.214850,11.228623,11.241821,11.254510,11.266747,11.278579,11.290048,11.301189,11.312033,11.322607,11.332935,11.343039,11.352937,11.362648,11.372186,11.381565,11.390799,11.399900,11.408878,11.417743,11.426505,11.435173,11.443755,11.452258,11.460690,11.469058,11.477368,11.485627,11.493840,11.502014,11.510154,11.518266,11.526354,11.534424,11.542482,11.550532,11.558580,11.566630,11.574688,11.582758,11.590847,11.598958,11.607098,11.615272,11.623485,11.631744,11.640054,11.648422,11.656854,11.665357,11.673939,11.682607,11.691369,11.700235,11.709213,11.718313,11.727547,11.736927,11.746465,11.756175,11.766073,11.776177,11.786505,11.797079,11.807923,11.819064,11.830533,11.842366,11.854602,11.867292,11.880489,11.894262,11.908690,11.923871,11.939927,11.957009,11.975313,11.995097,12.016712,12.040653,12.067650,12.098857,12.136263,12.183795,12.251255,12.381516
+cycle_on_powerlaw,365,2027-09-23,10.459584,10.644053,10.739588,10.806900,10.859873,10.904067,10.942299,10.976203,11.006813,11.034831,11.060752,11.084943,11.107680,11.129179,11.149611,11.169115,11.187805,11.205775,11.223105,11.239861,11.256103,11.271880,11.287237,11.302211,11.316837,11.331146,11.345164,11.358915,11.372422,11.385705,11.398782,11.411669,11.424384,11.436938,11.449347,11.461622,11.473775,11.485817,11.497759,11.509609,11.521377,11.533073,11.544704,11.556280,11.567807,11.579294,11.590748,11.602177,11.613588,11.624989,11.636385,11.647786,11.659197,11.670626,11.682080,11.693567,11.705095,11.716670,11.728301,11.739997,11.751765,11.763616,11.775557,11.787599,11.799752,11.812027,11.824436,11.836991,11.849705,11.862592,11.875669,11.888952,11.902459,11.916211,11.930228,11.944537,11.959163,11.974137,11.989494,12.005271,12.021513,12.038270,12.055599,12.073569,12.092259,12.111763,12.132196,12.153695,12.176431,12.200622,12.226543,12.254561,12.285171,12.319075,12.357307,12.401501,12.454474,12.521787,12.617321,12.801790
+cycle_on_powerlaw,730,2028-09-22,10.483953,10.744833,10.879939,10.975133,11.050048,11.112548,11.166616,11.214563,11.257853,11.297476,11.334134,11.368345,11.400499,11.430904,11.459799,11.487383,11.513814,11.539227,11.563735,11.587432,11.610402,11.632714,11.654432,11.675609,11.696293,11.716528,11.736352,11.755800,11.774902,11.793686,11.812180,11.830406,11.848387,11.866142,11.883690,11.901050,11.918237,11.935267,11.952154,11.968913,11.985556,12.002096,12.018545,12.034916,12.051218,12.067463,12.083662,12.099825,12.115962,12.132085,12.148202,12.164325,12.180462,12.196626,12.212824,12.229070,12.245372,12.261742,12.278191,12.294731,12.311374,12.328133,12.345020,12.362050,12.379237,12.396597,12.414146,12.431901,12.449881,12.468107,12.486601,12.505386,12.524488,12.543935,12.563759,12.583994,12.604679,12.625856,12.647573,12.669885,12.692855,12.716552,12.741060,12.766473,12.792905,12.820488,12.849384,12.879788,12.911943,12.946153,12.982811,13.022434,13.065724,13.113671,13.167740,13.230240,13.305154,13.400349,13.535454,13.796334
+cycle_on_powerlaw,1095,2029-09-22,10.671517,10.991027,11.156497,11.273086,11.364838,11.441384,11.507604,11.566327,11.619346,11.667874,11.712771,11.754670,11.794052,11.831289,11.866679,11.900461,11.932833,11.963958,11.993973,12.022997,12.051128,12.078456,12.105054,12.130990,12.156324,12.181107,12.205386,12.229204,12.252599,12.275605,12.298255,12.320578,12.342599,12.364345,12.385837,12.407098,12.428148,12.449005,12.469688,12.490213,12.510597,12.530854,12.551000,12.571050,12.591015,12.610912,12.630751,12.650547,12.670311,12.690057,12.709797,12.729543,12.749307,12.769103,12.788943,12.808839,12.828805,12.848854,12.869000,12.889257,12.909641,12.930166,12.950849,12.971706,12.992756,13.014017,13.035510,13.057255,13.079277,13.101599,13.124249,13.147256,13.170650,13.194468,13.218748,13.243531,13.268864,13.294800,13.321399,13.348726,13.376857,13.405881,13.435896,13.467021,13.499393,13.533175,13.568565,13.605803,13.645184,13.687083,13.731980,13.780508,13.833527,13.892250,13.958470,14.035017,14.126768,14.243357,14.408827,14.728338
+cycle_on_powerlaw,1460,2030-09-22,10.110988,10.479927,10.670995,10.805621,10.911566,10.999954,11.076419,11.144226,11.205447,11.261482,11.313325,11.361706,11.407180,11.450178,11.491042,11.530051,11.567431,11.603371,11.638030,11.671543,11.704026,11.735581,11.766294,11.796243,11.825495,11.854112,11.882147,11.909650,11.936664,11.963230,11.989384,12.015159,12.040588,12.065697,12.090515,12.115065,12.139371,12.163455,12.187337,12.211038,12.234575,12.257966,12.281229,12.304380,12.327434,12.350408,12.373317,12.396175,12.418997,12.441798,12.464591,12.487392,12.510214,12.533072,12.555981,12.578955,12.602010,12.625160,12.648423,12.671814,12.695351,12.719052,12.742934,12.767018,12.791324,12.815874,12.840692,12.865801,12.891230,12.917005,12.943159,12.969725,12.996739,13.024242,13.052277,13.080894,13.110146,13.140095,13.170808,13.202363,13.234846,13.268360,13.303018,13.338958,13.376338,13.415347,13.456212,13.499210,13.544683,13.593064,13.644907,13.700942,13.762163,13.829970,13.906435,13.994823,14.100768,14.235394,14.426462,14.795401

data/investing.csv

@@ -1,27 +1,5 @@
 "Date","Price","Open","High","Low","Vol.","Change %"
-"12/19/2024","97,466.1","100,190.5","102,778.8","95,672.2","200.57K","-2.73%"
+"11/27/2024","92,699.5","91,975.5","93,024.5","91,795.5","125.81K","0.78%"
-"12/18/2024","100,197.8","106,140.7","106,477.6","100,049.3","187.49K","-5.60%"
-"12/17/2024","106,138.9","106,053.4","108,244.9","105,350.6","149.37K","0.08%"
-"12/16/2024","106,057.6","104,479.2","107,767.6","103,351.7","232.66K","1.55%"
-"12/15/2024","104,443.0","101,417.9","105,120.9","101,234.9","133.99K","2.98%"
-"12/14/2024","101,417.7","101,423.7","102,633.0","100,626.3","105.31K","-0.01%"
-"12/13/2024","101,426.2","100,008.3","101,891.2","99,214.2","162.40K","1.42%"
-"12/12/2024","100,009.9","101,126.3","102,495.3","99,334.5","188.96K","-1.10%"
-"12/11/2024","101,126.2","96,603.2","101,877.1","95,689.5","250.02K","4.69%"
-"12/10/2024","96,600.3","97,311.5","98,237.8","94,304.5","271.45K","-0.78%"
-"12/09/2024","97,359.4","101,129.7","101,198.6","94,395.8","321.01K","-3.72%"
-"12/08/2024","101,115.8","99,837.0","101,339.9","98,713.9","128.93K","1.28%"
-"12/07/2024","99,837.0","99,757.2","100,441.8","98,969.0","118.44K","0.08%"
-"12/06/2024","99,760.7","96,968.9","101,908.5","96,452.0","213.49K","2.88%"
-"12/05/2024","96,970.8","98,624.8","103,719.4","92,510.4","245.79K","-1.69%"
-"12/04/2024","98,635.8","95,900.1","99,030.7","94,625.3","113.77K","2.85%"
-"12/03/2024","95,898.7","95,843.9","96,245.0","93,646.1","95.08K","0.05%"
-"12/02/2024","95,846.6","97,199.3","98,082.0","94,510.6","95.80K","-1.39%"
-"12/01/2024","97,201.4","96,404.7","97,813.9","95,721.8","42.90K","0.83%"
-"11/30/2024","96,405.7","97,438.5","97,461.9","96,119.6","36.92K","-1.06%"
-"11/29/2024","97,438.0","95,645.6","98,599.8","95,405.7","76.54K","1.87%"
-"11/28/2024","95,645.5","95,881.4","96,549.0","94,648.8","68.17K","-0.25%"
-"11/27/2024","95,886.6","91,975.5","97,219.8","91,795.5","106.39K","4.25%"
 "11/26/2024","91,977.6","93,046.5","94,978.8","90,817.2","131.88K","-1.17%"
 "11/25/2024","93,064.4","97,948.8","98,872.4","92,875.3","124.98K","-4.97%"
 "11/24/2024","97,935.2","97,696.4","98,552.6","95,765.4","77.04K","0.24%"

docs/2024-ideas.md

@@ -0,0 +1,65 @@
+# Ideas in the 2024 model's history
+
+A catalogue of the modeling ideas in the old `model.py` and its branches
+(September 2026). Labels are referenced from `btcmodel/experiments.py`.
+"Fudge" means the constant or rule existed to hit backtest coverage/MAPE
+targets rather than to express a hypothesis.
+
+## Drift
+
+- **D1. Mean return by halving-cycle position.** The core idea throughout
+  (initial commit, `Switch to simpler log-based projection`, `Implement trend
+  smoothing`, `tuning-b`). Smoothing went Savitzky-Golay → 60-day centred mean
+  → Gaussian kernel with recency weights. The old code stretched every cycle
+  to 1460 days (phase = fraction of the halving interval). Bugs: simple
+  returns compounded as log returns (+~25%/yr bias) in the initial commit;
+  genesis date off by a year; `tuning-3` regressed log price on row index
+  across cycles. The "blend ratio of 0 is best?" commit was blending the
+  simple- and log-return versions of the same quantity.
+- **D2. Drift damping.** Constants everywhere (×0.6–0.9, asymmetric, era- and
+  cycle-position-keyed, a 3%/day cap, the fundamentals ×0.65–0.75). Fudge as
+  implemented; the hypothesis underneath (the cycle drift is overfit) is real.
+- **D3. Diminishing returns.** Initial commit decayed drift by 0.9^(t/365);
+  `old/backtests-trend-enhancement-1` regressed per-cycle returns on cycle
+  number, but added that on top of the cycle drift (double counting) and
+  clipped paths.
+- **D4. "Skew".** `loc += sign(μ)·0.087σ`, tuned so 68% coverage hit 68.1%.
+  A fudge; its honest cousin is momentum.
+- **D5. Stock-to-flow.** A 30% blend of the daily % change in S2F into the
+  drift. Broken: mismatched units, and S2F "halvings" on the wrong dates
+  created a large fake post-halving drift.
+
+## Volatility
+
+- **V1. EWMA blend.** 30/90/180-day spans, weights .5/.3/.2 then .2/.5/.3,
+  times a 1.2 fudge.
+- **V2. Adaptive windows / regime weights.** Short/long vol ratio rescales
+  window lengths and blend weights; over-parameterised, and after the
+  fundamentals rewrite the adaptive windows were computed but unused.
+- **V3. Cycle-position volatility.** `old/backtest-vol-cycle`.
+- **V4. Market maturity.** Volume growth, inverse vol, autocorrelation and a
+  post-futures dummy, min-max normalised in-sample. Removed as "complexity
+  without clear benefit".
+- **V5. "Fundamentals".** Supply growth, volume/supply and "depth" combined
+  and clipped to [0.65, 0.75]: effectively a constant, grid-searched to match
+  the era constants it replaced.
+- **V6. Market conditions.** Vol ratio, MA50−MA200 trend strength (≈30× too
+  large from a units bug) and drawdown widening uncertainty.
+
+## Calibration (all fudges)
+
+- **C1. Era scaling keyed to the backtest's training start date**, with stacked
+  factors (net ≈0.45× vol) and hand-picked era boundaries.
+- **C2. Horizon uncertainty multipliers**, caps and floors on daily vol.
+- **C3. Changing the quantile levels**: a "95%" band read off the ~81%
+  quantiles past a year.
+
+## Shape
+
+- **S1. Skewed innovations**, with skew set per era (`tuning-1`).
+
+## Also
+
+Plumbing (backtest framework, multiprocessing, output handling, cycle and
+CDPR plots). The old NOTES.md described "machine learning" and "macro
+indicator" experiments; no such code ever existed.

flake.lock

@@ -0,0 +1,27 @@
+{
+  "nodes": {
+    "nixpkgs": {
+      "locked": {
+        "lastModified": 1790178388,
+        "narHash": "sha256-kK3t7gwoz4Nx8RF46cs1Xz/skKNcK7y3KYP+gGqX6W8=",
+        "owner": "NixOS",
+        "repo": "nixpkgs",
+        "rev": "00455b0a3690d3f5dc61e9aef4277dc86235b73f",
+        "type": "github"
+      },
+      "original": {
+        "owner": "NixOS",
+        "ref": "nixpkgs-unstable",
+        "repo": "nixpkgs",
+        "type": "github"
+      }
+    },
+    "root": {
+      "inputs": {
+        "nixpkgs": "nixpkgs"
+      }
+    }
+  },
+  "root": "root",
+  "version": 7
+}

flake.nix

@@ -0,0 +1,36 @@
+{
+  description = "Bitcoin price model";
+
+  inputs.nixpkgs.url = "github:NixOS/nixpkgs/nixpkgs-unstable";
+
+  outputs =
+    { self, nixpkgs }:
+    let
+      systems = [
+        "aarch64-darwin"
+        "x86_64-darwin"
+        "aarch64-linux"
+        "x86_64-linux"
+      ];
+      forAllSystems = f: nixpkgs.lib.genAttrs systems (system: f nixpkgs.legacyPackages.${system});
+    in
+    {
+      devShells = forAllSystems (pkgs: {
+        default = pkgs.mkShell {
+          packages = [
+            (pkgs.python313.withPackages (ps: [
+              ps.numpy
+              ps.pandas
+              ps.scipy
+              ps.matplotlib
+              ps.pytest
+            ]))
+            pkgs.ruff
+            pkgs.just
+          ];
+        };
+      });
+
+      formatter = forAllSystems (pkgs: pkgs.nixfmt);
+    };
+}

justfile

@@ -1,11 +1,49 @@
-run *name:
+# List recipes
-    python3 ./model.py -n "{{ name }}"
+default:
+    @just --list
+
+# Fetch new daily prices from Coinbase
+update:
+    python -m btcmodel update
+
+# Score models on development data (outcomes up to the dev cutoff)
+backtest *args:
+    python -m btcmodel {{ args }} backtest
+
+# Score models on held-out outcomes; run sparingly, never while tuning
+holdout *args:
+    python -m btcmodel {{ args }} backtest --holdout
+
+# Forecast from the latest price
+forecast *args:
+    python -m btcmodel {{ args }} forecast
+
+test:
+    pytest -q
 
 fmt:
-    black ./*.py
+    ruff format .
+    ruff check --fix --select I .
+    nix fmt flake.nix
 
 lint:
-    ruff check ./model.py
+    ruff check .
+    ruff format --check .
 
 clean:
     rm -rf output
+
+# Run A/B experiments on development data (default: all)
+ab *names:
+    python -m btcmodel ab {{ names }}
+
+# Record tracked models' forecasts for the forward test (commit the new file)
+snapshot:
+    python -m btcmodel snapshot
+
+# Score recorded forecasts whose target dates have passed
+forward:
+    python -m btcmodel forward
+
+# The weekly routine: new prices, a new snapshot, and scores so far
+weekly: update snapshot forward

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-
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-
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pyproject.toml

@@ -1,18 +1,24 @@
-[tool.poetry]
+[project]
-name = "bitcoin-model"
+name = "btcmodel"
-version = "0.1.0"
+version = "0.2.0"
-description = ""
+description = "Probabilistic Bitcoin price model"
-authors = ["Anthropic Claude <[email protected]>", "Sam Fredrickson <[email protected]>"]
+authors = [
+    { name = "Anthropic Claude", email = "[email protected]" },
+    { name = "Sam Fredrickson", email = "[email protected]" },
+]
 readme = "README.md"
+requires-python = ">=3.13"
+dependencies = ["numpy>=2", "pandas>=3", "scipy>=1.14", "matplotlib>=3.9"]
 
-[tool.poetry.dependencies]
+[dependency-groups]
-python = "^3.13"
+dev = ["pytest", "ruff"]
-pandas = "^2.2.3"
-matplotlib = "^3.9.2"
-seaborn = "^0.13.2"
-scipy = "^1.14.1"
 
+[tool.ruff]
+line-length = 100
 
-[build-system]
+[tool.ruff.lint]
-requires = ["poetry-core"]
+select = ["E", "F", "I", "B", "UP"]
-build-backend = "poetry.core.masonry.api"
+
+[tool.pytest.ini_options]
+testpaths = ["tests"]
+pythonpath = ["."]

tests/test_components.py

@@ -0,0 +1,85 @@
+import numpy as np
+import pandas as pd
+import pytest
+
+from btcmodel.experiments import EXPERIMENTS
+from btcmodel.halving import GENESIS
+from btcmodel.models.drift import CycleDrift, PowerLawDrift, ShrunkDrift
+from btcmodel.models.shape import StudentT
+from btcmodel.models.volatility import ReversionVol, TrailingVol, TrendReversionVol
+
+from .test_models import synthetic_prices
+
+ALL_VARIANTS = {m.name: m for e in EXPERIMENTS.values() for m in e.models}
+
+
+@pytest.mark.parametrize("name", list(ALL_VARIANTS))
+def test_experiment_models_produce_valid_forecasts(name):
+    prices = synthetic_prices(lambda day: 0.001 + 0 * day, noise=0.03)
+    horizons = np.array([1, 30, 365, 1460])
+    f = ALL_VARIANTS[name].forecast(prices, horizons)
+    assert np.isfinite(f.log_quantiles).all()
+    assert np.all(np.diff(f.log_quantiles, axis=1) >= 0)
+    lo, hi = f.interval(0.8)
+    assert np.all(np.diff(hi - lo) > 0)
+
+
+def test_shrunk_drift_scales_linearly():
+    prices = synthetic_prices(lambda day: np.where(day < 700, 0.002, -0.001))
+    horizons = np.array([100, 1000])
+    full = CycleDrift().expected_log_return(prices, horizons)
+    np.testing.assert_allclose(
+        ShrunkDrift(CycleDrift(), 0.5).expected_log_return(prices, horizons), full / 2
+    )
+    np.testing.assert_allclose(
+        ShrunkDrift(CycleDrift(), 0.0).expected_log_return(prices, horizons), 0
+    )
+
+
+def test_power_law_recovers_its_exponent():
+    dates = pd.date_range("2011-01-01", "2024-11-26", freq="D", name="date")
+    t = (dates - GENESIS).days.to_numpy()
+    prices = pd.DataFrame({"close": 1e-17 * t**5.8}, index=dates)
+    _, slope, _ = PowerLawDrift().fit(prices)
+    assert slope == pytest.approx(5.8, rel=1e-6)
+    expected = 5.8 * np.log((t[-1] + 365) / t[-1])
+    assert PowerLawDrift().expected_log_return(prices, np.array([365]))[0] == pytest.approx(
+        expected
+    )
+
+
+def test_reversion_vol_matches_trailing_when_already_at_long_run():
+    rng = np.random.default_rng(0)
+    dates = pd.date_range("2011-01-01", "2024-11-26", freq="D", name="date")
+    prices = pd.DataFrame(
+        {"close": 100 * np.exp(np.cumsum(0.03 * rng.standard_normal(len(dates))))}, index=dates
+    )
+    horizons = np.array([30, 365, 1460])
+    reverting = ReversionVol(now_span=1460, long_window=len(dates)).sd(prices, horizons)
+    flat = TrailingVol(window=len(dates)).sd(prices, horizons)
+    np.testing.assert_allclose(reverting, flat, rtol=0.05)
+
+
+def test_student_t_shape_has_unit_variance_and_fatter_tails():
+    q = StudentT(4).standard_quantiles(None, np.array([1]))[0]
+    assert q[-1] > 2.576  # beyond the normal 99.5% quantile
+    assert np.interp(0.8413, np.linspace(0.005, 0.995, 100), q) < 1.0  # thinner shoulders
+
+
+def test_trend_reversion_vol_levels_off():
+    # A power-law trend plus AR(1) deviations with a ~70-day half-life.
+    rng = np.random.default_rng(0)
+    dates = pd.date_range("2011-01-01", "2024-11-26", freq="D", name="date")
+    t = (dates - GENESIS).days.to_numpy()
+    gap = np.zeros(len(t))
+    for i in range(1, len(t)):
+        gap[i] = 0.99 * gap[i - 1] + 0.03 * rng.standard_normal()
+    prices = pd.DataFrame({"close": np.exp(-40 + 5.8 * np.log(t) + gap)}, index=dates)
+
+    horizons = np.array([30, 365, 1460, 5000])
+    plain = TrendReversionVol().sd(prices, horizons)
+    with_params = TrendReversionVol(parameter_uncertainty=True).sd(prices, horizons)
+    assert np.all(np.diff(plain) >= 0)
+    stationary = 0.03 / np.sqrt(1 - 0.99**2)
+    assert plain[-1] == pytest.approx(stationary, rel=0.15)
+    assert np.all(with_params >= plain)

tests/test_forecast.py

@@ -0,0 +1,44 @@
+import numpy as np
+import pandas as pd
+from scipy.stats import norm
+
+from btcmodel.forecast import Forecast, crps, pit
+
+
+def normal_crps(mu, sigma, y):
+    """Closed-form CRPS of N(mu, sigma^2) at y."""
+    z = (y - mu) / sigma
+    return sigma * (z * (2 * norm.cdf(z) - 1) + 2 * norm.pdf(z) - 1 / np.sqrt(np.pi))
+
+
+def test_crps_matches_closed_form_for_normal():
+    f = Forecast.normal("2020-01-01", np.array([1, 2, 3]), mean=[0.0, 1.0, 2.0], sd=[1.0, 0.5, 2.0])
+    y = np.array([0.3, -0.2, 5.0])
+    expected = normal_crps(np.array([0.0, 1.0, 2.0]), np.array([1.0, 0.5, 2.0]), y)
+    np.testing.assert_allclose(crps(f.log_quantiles, y), expected, rtol=0.02)
+
+
+def test_crps_prefers_the_right_forecast():
+    y = np.array([0.0])
+    good = Forecast.normal("2020-01-01", np.array([1]), 0.0, 0.1)
+    biased = Forecast.normal("2020-01-01", np.array([1]), 0.5, 0.1)
+    vague = Forecast.normal("2020-01-01", np.array([1]), 0.0, 2.0)
+    assert crps(good.log_quantiles, y) < crps(biased.log_quantiles, y)
+    assert crps(good.log_quantiles, y) < crps(vague.log_quantiles, y)
+
+
+def test_pit_and_intervals():
+    f = Forecast.normal("2020-01-01", np.array([1, 1, 1]), 0.0, 1.0)
+    np.testing.assert_allclose(
+        pit(f.log_quantiles, [0.0, 1.0, -10.0]), [0.5, 0.841, 0.0], atol=0.01
+    )
+    lo, hi = f.interval(0.95)
+    np.testing.assert_allclose(hi, 1.96, atol=0.01)
+    np.testing.assert_allclose(lo, -1.96, atol=0.01)
+
+
+def test_from_samples_recovers_quantiles():
+    rng = np.random.default_rng(0)
+    f = Forecast.from_samples("2020-01-01", np.array([10]), rng.normal(0, 1, size=(200_000, 1)))
+    np.testing.assert_allclose(f.quantile(0.5), 0.0, atol=0.02)
+    assert f.dates[0] == pd.Timestamp("2020-01-11")

tests/test_forward.py

@@ -0,0 +1,57 @@
+import numpy as np
+import pandas as pd
+import pytest
+
+from btcmodel import forward
+from btcmodel.evaluate import HORIZONS, score
+from btcmodel.models import MODELS
+
+from .test_models import synthetic_prices
+
+MODELS_UNDER_TEST = [MODELS["random_walk"], MODELS["powerlaw"]]
+
+
+@pytest.fixture
+def prices():
+    return synthetic_prices(lambda day: 0.001 + 0 * day, end="2025-03-31", noise=0.03)
+
+
+def test_snapshot_records_every_model_and_horizon(prices, tmp_path):
+    history = prices.loc[:"2024-11-26"]
+    path = forward.snapshot(history, MODELS_UNDER_TEST, tmp_path, pd.Timestamp("2024-11-27"))
+    recorded = pd.read_csv(path)
+    assert path.name == "2024-11-26.csv"
+    assert len(recorded) == len(MODELS_UNDER_TEST) * len(HORIZONS)
+    assert recorded.target.iloc[0] == "2024-12-26"
+
+
+def test_snapshot_refuses_stale_data_and_duplicates(prices, tmp_path):
+    history = prices.loc[:"2024-11-26"]
+    with pytest.raises(ValueError, match="real time"):
+        forward.snapshot(history, MODELS_UNDER_TEST, tmp_path, pd.Timestamp("2024-12-10"))
+    forward.snapshot(history, MODELS_UNDER_TEST, tmp_path, pd.Timestamp("2024-11-27"))
+    with pytest.raises(FileExistsError):
+        forward.snapshot(history, MODELS_UNDER_TEST, tmp_path, pd.Timestamp("2024-11-27"))
+
+
+def test_scores_only_due_horizons_and_match_the_backtest(prices, tmp_path):
+    history = prices.loc[:"2024-11-26"]
+    forward.snapshot(history, MODELS_UNDER_TEST, tmp_path, pd.Timestamp("2024-11-27"))
+
+    assert forward.score_snapshots(prices.loc[:"2024-12-20"], tmp_path).empty
+    assert forward.next_due(prices.loc[:"2024-12-20"], tmp_path) == pd.Timestamp("2024-12-26")
+
+    scores = forward.score_snapshots(prices, tmp_path)
+    assert sorted(scores.horizon.unique()) == [30, 91]
+
+    model = MODELS["powerlaw"]
+    horizons = np.array([30, 91])
+    direct = score(
+        "powerlaw",
+        model.forecast(history, horizons),
+        np.log(
+            prices.close.loc[history.index[-1] + pd.to_timedelta(horizons, unit="D")]
+        ).to_numpy(),
+    )
+    recorded = scores[scores.model == "powerlaw"].sort_values("horizon")
+    np.testing.assert_allclose(recorded.crps, direct.crps, atol=1e-5)

tests/test_models.py

@@ -0,0 +1,83 @@
+import numpy as np
+import pandas as pd
+import pytest
+
+from btcmodel import data
+from btcmodel.evaluate import backtest
+from btcmodel.halving import HALVINGS, cycle_position
+from btcmodel.models import MODELS, CycleDrift
+
+
+def synthetic_prices(daily_return, start="2011-01-01", end="2024-11-26", noise=0.0, seed=0):
+    """Prices whose daily log return is `daily_return(cycle_day)` plus optional noise."""
+    dates = pd.date_range(start, end, freq="D", name="date")
+    _, day = cycle_position(dates)
+    r = daily_return(day) + noise * np.random.default_rng(seed).standard_normal(len(dates))
+    return pd.DataFrame({"close": 100 * np.exp(np.cumsum(r))}, index=dates)
+
+
+def test_cycle_position():
+    index, day = cycle_position(pd.DatetimeIndex(["2009-01-03", "2012-11-27", *HALVINGS]))
+    assert list(index) == [0, 0, 1, 2, 3, 4]
+    assert list(day) == [0, 1424, 0, 0, 0, 0]
+    # A projected halving about four years after the last one starts cycle 5.
+    index, _ = cycle_position(pd.DatetimeIndex(["2028-06-01"]))
+    assert index[0] == 5
+
+
+def test_cycle_model_recovers_a_cycle_shaped_drift():
+    # Up for the first half of each cycle, down in the second half.
+    def shape(day):
+        return np.where(day < 700, 0.002, -0.001)
+
+    prices = synthetic_prices(shape)
+    drift = CycleDrift(prior_days=0).by_cycle_day(prices)
+    assert drift[300] == pytest.approx(0.002, abs=2e-4)
+    assert drift[1100] == pytest.approx(-0.001, abs=2e-4)
+
+
+def test_cycle_model_weights_recent_cycles_more():
+    # The same day of the cycle returns less in each later cycle.
+    prices = synthetic_prices(lambda day: np.zeros_like(day, dtype=float))
+    cycle, _ = cycle_position(prices.index)
+    r = 0.004 / 2.0**cycle
+    prices["close"] = 100 * np.exp(np.cumsum(r))
+    drift = CycleDrift(recency_half_life=0.25).by_cycle_day(prices)
+    equal = CycleDrift(recency_half_life=1e9).by_cycle_day(prices)
+    latest_complete = 0.004 / 2.0**3
+    assert abs(drift[900] - latest_complete) < abs(equal[900] - latest_complete)
+
+
+@pytest.mark.parametrize("name", list(MODELS))
+def test_models_produce_valid_forecasts(name):
+    prices = synthetic_prices(lambda day: 0.001 + 0 * day, noise=0.03)
+    horizons = np.array([1, 30, 365, 1460])
+    f = MODELS[name].forecast(prices, horizons)
+    assert f.log_quantiles.shape == (4, 100)
+    assert np.all(np.diff(f.log_quantiles, axis=1) >= 0)
+    lo, hi = f.interval(0.8)
+    assert np.all(np.diff(hi - lo) > 0), "uncertainty should grow with horizon"
+
+
+def test_backtest_never_shows_models_the_future():
+    prices = synthetic_prices(lambda day: 0.001 + 0 * day, noise=0.03)
+
+    class Spy:
+        name = "random_walk"
+
+        def forecast(self, history, horizons):
+            origin = history.index[-1]
+            assert history.index.max() == origin
+            assert (origin + pd.Timedelta(days=int(horizons.min()))) > history.index.max()
+            return MODELS["random_walk"].forecast(history, horizons)
+
+    scores = backtest([Spy()], prices)
+    assert len(scores) > 0
+    targets = scores.origin + pd.to_timedelta(scores.horizon, unit="D")
+    assert targets.max() <= prices.index[-1]
+
+
+def test_development_data_stops_at_cutoff():
+    prices = data.load_prices(until=data.DEV_CUTOFF)
+    assert prices.index[0] == data.DATA_START
+    assert prices.index[-1] == data.DEV_CUTOFF