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