1016 lines
33 KiB
Python
1016 lines
33 KiB
Python
import pandas as pd
|
|
import numpy as np
|
|
from datetime import datetime, timedelta
|
|
import matplotlib.pyplot as plt
|
|
import seaborn as sns
|
|
from scipy.stats import norm
|
|
from scipy.signal import savgol_filter
|
|
|
|
|
|
# Utility functions
|
|
|
|
|
|
def get_halving_dates():
|
|
"""Return known and projected Bitcoin halving dates"""
|
|
return pd.to_datetime(
|
|
[
|
|
"2008-01-03", # Bitcoin genesis block (treat as cycle start)
|
|
"2012-11-28", # First halving
|
|
"2016-07-09", # Second halving
|
|
"2020-05-11", # Third halving
|
|
"2024-04-19", # Fourth halving
|
|
"2028-04-20", # Fifth halving (projected)
|
|
]
|
|
)
|
|
|
|
|
|
def get_cycle_position(date, halving_dates):
|
|
"""
|
|
Calculate position in halving cycle (0 to 1) for a given date.
|
|
0 represents a halving event, 1 represents just before the next halving.
|
|
"""
|
|
# Convert date to datetime if it's not already
|
|
date = pd.to_datetime(date)
|
|
|
|
# Find the most recent halving before this date
|
|
prev_halving = halving_dates[halving_dates <= date].max()
|
|
if pd.isna(prev_halving):
|
|
return 0.0 # For dates before first halving
|
|
|
|
# Find next halving
|
|
future_halvings = halving_dates[halving_dates > date]
|
|
if len(future_halvings) == 0:
|
|
# For dates after last known halving, use same cycle length as last known cycle
|
|
last_cycle_length = (halving_dates[-1] - halving_dates[-2]).days
|
|
days_since_halving = (date - halving_dates[-1]).days
|
|
return min(days_since_halving / last_cycle_length, 1.0)
|
|
|
|
next_halving = future_halvings.min()
|
|
|
|
# Calculate position as fraction between halvings
|
|
days_since_halving = (date - prev_halving).days
|
|
cycle_length = (next_halving - prev_halving).days
|
|
return min(days_since_halving / cycle_length, 1.0)
|
|
|
|
|
|
def format_price(x, p):
|
|
"""Format large numbers in K, M, B format with appropriate precision"""
|
|
if abs(x) >= 1e9:
|
|
return f"${x/1e9:.1f}B"
|
|
if abs(x) >= 1e6:
|
|
return f"${x/1e6:.1f}M"
|
|
if abs(x) >= 1e3:
|
|
return f"${x/1e3:.1f}K"
|
|
if abs(x) >= 1:
|
|
return f"${x:.0f}"
|
|
return f"${x:.2f}" # For values less than $1, show cents
|
|
|
|
|
|
def get_nice_price_points(min_price, max_price):
|
|
"""
|
|
Generate a reasonable set of price points for the y-axis that look clean
|
|
and cover the range without cluttering the chart.
|
|
"""
|
|
# Handle zero or negative prices
|
|
min_price = max(min_price, 0.0001) # Set minimum price to $0.0001
|
|
|
|
log_min = np.floor(np.log10(min_price))
|
|
log_max = np.ceil(np.log10(max_price))
|
|
price_points = []
|
|
|
|
# For very large ranges (spanning more than 4 orders of magnitude),
|
|
# only use powers of 10 and mid-points
|
|
if log_max - log_min > 4:
|
|
for exp in range(int(log_min), int(log_max + 1)):
|
|
base = 10**exp
|
|
# Add main power of 10
|
|
if min_price <= base <= max_price:
|
|
price_points.append(base)
|
|
# Add mid-point if range is large enough
|
|
if min_price <= base * 5 <= max_price and exp > log_min:
|
|
price_points.append(base * 5)
|
|
else:
|
|
# For smaller ranges, use 1, 2, 5 sequence
|
|
for exp in range(int(log_min), int(log_max + 1)):
|
|
for mult in [1, 2, 5]:
|
|
point = mult * 10**exp
|
|
if min_price <= point <= max_price:
|
|
price_points.append(point)
|
|
|
|
return np.array(price_points)
|
|
|
|
|
|
# Analysis functions
|
|
|
|
|
|
def analyze_trends(df):
|
|
"""
|
|
Analyze Bitcoin price trends using log returns with simple moving average smoothing.
|
|
"""
|
|
df = df.copy()
|
|
|
|
# Get halving dates and calculate cycle position
|
|
halving_dates = get_halving_dates()
|
|
df["Cycle_Position"] = df["Date"].apply(
|
|
lambda x: get_cycle_position(x, halving_dates)
|
|
)
|
|
df["Cycle_Days"] = (df["Cycle_Position"] * 4 * 365).round().astype(int)
|
|
|
|
# Calculate log returns
|
|
df["Log_Price"] = np.log(df["Close"])
|
|
df["Log_Return"] = df["Log_Price"].diff()
|
|
|
|
# Group by position in cycle
|
|
position_returns = df.groupby("Cycle_Days")["Log_Return"].mean()
|
|
|
|
# Simple moving average smoothing
|
|
window = 60
|
|
smoothed_returns = position_returns.rolling(
|
|
window=window,
|
|
center=True, # Center the window for better trend capture
|
|
min_periods=int(window / 2), # Allow partial windows to reduce edge effects
|
|
).mean()
|
|
|
|
# Fill any NaN values at the edges
|
|
smoothed_returns = smoothed_returns.fillna(method="bfill").fillna(method="ffill")
|
|
|
|
return smoothed_returns
|
|
|
|
|
|
def calculate_volatility(df, short_window=30, medium_window=90, long_window=180):
|
|
"""
|
|
Calculate volatility using multiple timeframes and exponential weighting.
|
|
Returns a more nuanced estimate of current market volatility.
|
|
"""
|
|
df = df.copy()
|
|
|
|
# Calculate log returns if not already present
|
|
if "Log_Return" not in df.columns:
|
|
df["Log_Price"] = np.log(df["Close"])
|
|
df["Log_Return"] = df["Log_Price"].diff()
|
|
|
|
# Calculate exponentially weighted volatilities for different timeframes
|
|
short_vol = df["Log_Return"].ewm(span=short_window).std().iloc[-1]
|
|
medium_vol = df["Log_Return"].ewm(span=medium_window).std().iloc[-1]
|
|
long_vol = df["Log_Return"].ewm(span=long_window).std().iloc[-1]
|
|
|
|
# Blend the estimates with more weight on recent data
|
|
base_vol = 0.5 * short_vol + 0.3 * medium_vol + 0.2 * long_vol
|
|
|
|
# Scale up volatility to target ~68% coverage
|
|
volatility_scale = 1.2
|
|
return base_vol * volatility_scale
|
|
|
|
|
|
def project_prices(
|
|
df, days_forward=365, simulations=1000, confidence_levels=[0.95, 0.68]
|
|
):
|
|
"""
|
|
Project future Bitcoin prices using Monte Carlo simulation.
|
|
Uses enhanced trend smoothing for better predictions.
|
|
"""
|
|
# Calculate log returns for volatility estimation
|
|
df = df.copy()
|
|
df["Log_Price"] = np.log(df["Close"])
|
|
df["Log_Return"] = df["Log_Price"].diff()
|
|
|
|
# Get smoothed trends
|
|
cycle_trends = analyze_trends(df)
|
|
|
|
# Get current position in halving cycle
|
|
halving_dates = get_halving_dates()
|
|
current_date = df["Date"].max()
|
|
cycle_position = get_cycle_position(current_date, halving_dates)
|
|
current_cycle_days = int(cycle_position * 4 * 365)
|
|
|
|
# Current price and date
|
|
last_price = df["Close"].iloc[-1]
|
|
last_date = df["Date"].iloc[-1]
|
|
|
|
# Generate dates for projection
|
|
future_dates = pd.date_range(
|
|
start=last_date + timedelta(days=1), periods=days_forward, freq="D"
|
|
)
|
|
|
|
# Calculate expected returns with enhanced cycle boundary handling
|
|
future_cycle_days = [
|
|
(current_cycle_days + i) % (4 * 365) for i in range(days_forward)
|
|
]
|
|
expected_returns = []
|
|
|
|
for day in future_cycle_days:
|
|
# Get base trend value
|
|
base_trend = cycle_trends.get(day, cycle_trends.mean())
|
|
|
|
# Add slight mean reversion for extreme values
|
|
if abs(base_trend) > 2 * cycle_trends.std():
|
|
base_trend *= 0.8 # Dampen extreme trends
|
|
|
|
expected_returns.append(base_trend)
|
|
|
|
expected_returns = np.array(expected_returns)
|
|
|
|
# Calculate volatility
|
|
volatility = calculate_volatility(df)
|
|
|
|
# Run Monte Carlo simulation
|
|
np.random.seed(42)
|
|
simulated_paths = np.zeros((days_forward, simulations))
|
|
|
|
for sim in range(simulations):
|
|
skew = np.sign(expected_returns) * 0.087 # Small skew in direction of trend
|
|
returns = np.random.normal(
|
|
loc=expected_returns + skew * volatility,
|
|
scale=volatility,
|
|
size=days_forward,
|
|
)
|
|
|
|
# Calculate price path
|
|
cumulative_returns = np.cumsum(returns)
|
|
price_path = last_price * np.exp(cumulative_returns)
|
|
simulated_paths[:, sim] = price_path
|
|
|
|
# Calculate percentiles for confidence intervals
|
|
results = pd.DataFrame(index=future_dates)
|
|
results["Median"] = np.percentile(simulated_paths, 50, axis=1)
|
|
|
|
for level in confidence_levels:
|
|
lower_percentile = (1 - level) * 100 / 2
|
|
upper_percentile = 100 - lower_percentile
|
|
|
|
results[f"Lower_{int(level*100)}"] = np.percentile(
|
|
simulated_paths, lower_percentile, axis=1
|
|
)
|
|
results[f"Upper_{int(level*100)}"] = np.percentile(
|
|
simulated_paths, upper_percentile, axis=1
|
|
)
|
|
|
|
# Add expected trend line
|
|
results["Expected_Trend"] = last_price * np.exp(np.cumsum(expected_returns))
|
|
|
|
return results
|
|
|
|
|
|
def analyze_bitcoin_prices(csv_path):
|
|
"""
|
|
Analyze Bitcoin price data to calculate volatility and growth rates.
|
|
"""
|
|
# Read CSV with proper data types
|
|
df = pd.read_csv(csv_path, parse_dates=[0])
|
|
|
|
# Print first few rows of raw data to inspect
|
|
print("\nFirst few rows of raw data:")
|
|
print(df.head())
|
|
|
|
# Print data info to see types and non-null counts
|
|
print("\nDataset Info:")
|
|
print(df.info())
|
|
|
|
# Convert price columns to float and handle any potential formatting issues
|
|
price_columns = ["Price", "Open", "High", "Low"]
|
|
for col in price_columns:
|
|
# Remove any commas in numbers
|
|
df[col] = df[col].astype(str).str.replace(",", "")
|
|
df[col] = pd.to_numeric(df[col], errors="coerce")
|
|
|
|
# Rename columns for clarity
|
|
df.columns = ["Date", "Close", "Open", "High", "Low", "Volume", "Change"]
|
|
|
|
# Sort by date in ascending order
|
|
df = df.sort_values("Date")
|
|
|
|
# Print summary statistics after conversion
|
|
print("\nPrice Summary After Conversion:")
|
|
print(df[["Close", "Open", "High", "Low"]].describe())
|
|
|
|
# Calculate daily returns
|
|
df["Daily_Return"] = df["Close"].pct_change()
|
|
|
|
# Print first few daily returns to verify calculation
|
|
print("\nFirst few daily returns:")
|
|
print(df[["Date", "Close", "Daily_Return"]].head())
|
|
|
|
# Check for any infinite or NaN values
|
|
print("\nInfinite or NaN value counts:")
|
|
print(df.isna().sum())
|
|
|
|
# Calculate metrics using 365 days for annualization
|
|
analysis = {
|
|
"period_start": df["Date"].min().strftime("%Y-%m-%d"),
|
|
"period_end": df["Date"].max().strftime("%Y-%m-%d"),
|
|
"total_days": len(df),
|
|
"daily_volatility": df["Daily_Return"].std(),
|
|
"annualized_volatility": df["Daily_Return"].std() * np.sqrt(365),
|
|
"total_return": (df["Close"].iloc[-1] / df["Close"].iloc[0] - 1) * 100,
|
|
"average_daily_return": df["Daily_Return"].mean() * 100,
|
|
"average_annual_return": ((1 + df["Daily_Return"].mean()) ** 365 - 1) * 100,
|
|
"min_price": df["Low"].min(),
|
|
"max_price": df["High"].max(),
|
|
"avg_price": df["Close"].mean(),
|
|
"start_price": df["Close"].iloc[0],
|
|
"end_price": df["Close"].iloc[-1],
|
|
}
|
|
|
|
# Calculate rolling metrics
|
|
df["Rolling_Volatility_30d"] = df["Daily_Return"].rolling(
|
|
window=30
|
|
).std() * np.sqrt(365)
|
|
df["Rolling_Return_30d"] = df["Close"].pct_change(periods=30) * 100
|
|
|
|
return analysis, df
|
|
|
|
|
|
# Main plotting functions
|
|
|
|
|
|
def create_plots(df, start=None, end=None, project_days=365):
|
|
"""
|
|
Create plots including historical data and future projections.
|
|
"""
|
|
# Filter data based on date range
|
|
mask = pd.Series(True, index=df.index)
|
|
if start:
|
|
mask &= df["Date"] >= pd.to_datetime(start)
|
|
if end:
|
|
mask &= df["Date"] <= pd.to_datetime(end)
|
|
|
|
plot_df = df[mask].copy()
|
|
|
|
if len(plot_df) == 0:
|
|
raise ValueError("No data found for the specified date range")
|
|
|
|
# Generate projections
|
|
# cycle_returns, cycle_volatility = analyze_trends(plot_df)
|
|
projections = project_prices(plot_df, days_forward=project_days)
|
|
|
|
# Create cycle visualization
|
|
# visualize_cycle_patterns(plot_df, cycle_returns, cycle_volatility)
|
|
|
|
# Set up the style
|
|
plt.style.use("seaborn-v0_8")
|
|
|
|
# Create figure
|
|
fig = plt.figure(figsize=(15, 15))
|
|
|
|
# Date range for titles
|
|
hist_date_range = f" ({plot_df['Date'].min().strftime('%Y-%m-%d')} to {plot_df['Date'].max().strftime('%Y-%m-%d')})"
|
|
|
|
# 1. Price history and projections (log scale)
|
|
ax1 = plt.subplot(4, 1, 1)
|
|
|
|
# Plot historical prices
|
|
ax1.semilogy(plot_df["Date"], plot_df["Close"], "b-", label="Historical Price")
|
|
|
|
# Plot projections
|
|
ax1.semilogy(
|
|
projections.index,
|
|
projections["Expected_Trend"],
|
|
"--",
|
|
color="purple",
|
|
label="Expected Trend",
|
|
)
|
|
ax1.semilogy(
|
|
projections.index,
|
|
projections["Median"],
|
|
":",
|
|
color="green",
|
|
label="Simulated Median",
|
|
)
|
|
ax1.fill_between(
|
|
projections.index,
|
|
projections["Lower_95"],
|
|
projections["Upper_95"],
|
|
alpha=0.2,
|
|
color="orange",
|
|
label="95% Confidence Interval",
|
|
)
|
|
ax1.fill_between(
|
|
projections.index,
|
|
projections["Lower_68"],
|
|
projections["Upper_68"],
|
|
alpha=0.3,
|
|
color="green",
|
|
label="68% Confidence Interval",
|
|
)
|
|
|
|
# Customize y-axis
|
|
ax1.yaxis.set_major_formatter(plt.FuncFormatter(format_price))
|
|
|
|
# Set custom y-axis ticks at meaningful price points
|
|
min_price = min(plot_df["Low"].min(), projections["Lower_95"].min())
|
|
max_price = max(plot_df["High"].max(), projections["Upper_95"].max())
|
|
|
|
price_points = get_nice_price_points(min_price, max_price)
|
|
ax1.set_yticks(price_points)
|
|
|
|
# Adjust y-axis label properties
|
|
ax1.tick_params(axis="y", labelsize=8) # Smaller font size
|
|
|
|
# Add some padding to prevent label cutoff
|
|
ax1.margins(y=0.02)
|
|
|
|
# Adjust label padding to prevent overlap
|
|
ax1.yaxis.set_tick_params(pad=1)
|
|
|
|
# Add grid lines with adjusted opacity
|
|
ax1.grid(True, which="major", linestyle="-", alpha=0.5)
|
|
ax1.grid(True, which="minor", linestyle=":", alpha=0.2)
|
|
|
|
ax1.set_title("Bitcoin Price History and Projections (Log Scale)" + hist_date_range)
|
|
# Make legend font size smaller too for consistency
|
|
ax1.legend(fontsize=8)
|
|
|
|
# 2. Rolling volatility
|
|
ax2 = plt.subplot(4, 1, 2)
|
|
ax2.plot(
|
|
plot_df["Date"],
|
|
plot_df["Rolling_Volatility_30d"],
|
|
"r-",
|
|
label="30-Day Rolling Volatility",
|
|
)
|
|
ax2.set_title("30-Day Rolling Volatility (Annualized)" + hist_date_range)
|
|
ax2.set_xlabel("Date")
|
|
ax2.set_ylabel("Volatility")
|
|
ax2.grid(True)
|
|
ax2.yaxis.set_major_formatter(plt.FuncFormatter(lambda y, _: "{:.0%}".format(y)))
|
|
ax2.legend()
|
|
|
|
# 3. Returns distribution
|
|
ax3 = plt.subplot(4, 1, 3)
|
|
returns_mean = plot_df["Daily_Return"].mean()
|
|
returns_std = plot_df["Daily_Return"].std()
|
|
filtered_returns = plot_df["Daily_Return"][
|
|
(plot_df["Daily_Return"] > returns_mean - 5 * returns_std)
|
|
& (plot_df["Daily_Return"] < returns_mean + 5 * returns_std)
|
|
]
|
|
|
|
sns.histplot(filtered_returns, bins=100, ax=ax3)
|
|
ax3.set_title(
|
|
"Distribution of Daily Returns (Excluding Extreme Outliers)" + hist_date_range
|
|
)
|
|
ax3.set_xlabel("Daily Return")
|
|
ax3.set_ylabel("Count")
|
|
ax3.xaxis.set_major_formatter(plt.FuncFormatter(lambda x, _: "{:.0%}".format(x)))
|
|
|
|
# Add a vertical line for mean return
|
|
ax3.axvline(filtered_returns.mean(), color="r", linestyle="dashed", linewidth=1)
|
|
ax3.text(
|
|
filtered_returns.mean(),
|
|
ax3.get_ylim()[1],
|
|
"Mean",
|
|
rotation=90,
|
|
va="top",
|
|
ha="right",
|
|
)
|
|
|
|
# 4. Projection ranges
|
|
ax4 = plt.subplot(4, 1, 4)
|
|
|
|
# Calculate and plot price ranges at different future points
|
|
timepoints = np.array(range(30, 365, 30))
|
|
timepoints = timepoints[timepoints <= project_days]
|
|
|
|
ranges = []
|
|
labels = []
|
|
positions = []
|
|
|
|
for t in timepoints:
|
|
idx = t - 1 # Convert to 0-based index
|
|
ranges.extend(
|
|
[
|
|
projections["Lower_95"].iloc[idx],
|
|
projections["Lower_68"].iloc[idx],
|
|
projections["Median"].iloc[idx],
|
|
projections["Upper_68"].iloc[idx],
|
|
projections["Upper_95"].iloc[idx],
|
|
]
|
|
)
|
|
labels.extend(["95% Lower", "68% Lower", "Median", "68% Upper", "95% Upper"])
|
|
positions.extend([t] * 5)
|
|
|
|
# Plot ranges (removed violin plot)
|
|
ax4.scatter(positions, ranges, alpha=0.6)
|
|
|
|
# Add lines connecting the ranges
|
|
for t in timepoints:
|
|
idx = positions.index(t)
|
|
ax4.plot([t] * 5, ranges[idx : idx + 5], "k-", alpha=0.3)
|
|
|
|
# Set log scale first
|
|
ax4.set_yscale("log")
|
|
|
|
# Get the current order of magnitude for setting appropriate ticks
|
|
min_price = min(ranges)
|
|
max_price = max(ranges)
|
|
|
|
# Create price points at regular intervals on log scale
|
|
log_min = np.floor(np.log10(min_price))
|
|
log_max = np.ceil(np.log10(max_price))
|
|
price_points = []
|
|
for exp in range(int(log_min), int(log_max + 1)):
|
|
for mult in [1, 2, 5]:
|
|
point = mult * 10**exp
|
|
if min_price <= point <= max_price:
|
|
price_points.append(point)
|
|
|
|
ax4.set_yticks(price_points)
|
|
|
|
def price_formatter(x, p):
|
|
if x >= 1e6:
|
|
return f"${x/1e6:.1f}M"
|
|
if x >= 1e3:
|
|
return f"${x/1e3:.0f}K"
|
|
return f"${x:.0f}"
|
|
|
|
# Apply formatter to major ticks
|
|
ax4.yaxis.set_major_formatter(plt.FuncFormatter(price_formatter))
|
|
|
|
# Customize the plot
|
|
ax4.set_title("Projected Price Ranges at Future Timepoints")
|
|
ax4.set_xlabel("Days Forward")
|
|
ax4.set_ylabel("Price (USD)")
|
|
ax4.grid(True, alpha=0.3)
|
|
|
|
# Set x-axis to show only our timepoints
|
|
ax4.set_xticks(timepoints)
|
|
|
|
# Adjust layout
|
|
plt.tight_layout()
|
|
|
|
# Save the plot
|
|
start_str = start if start else plot_df["Date"].min().strftime("%Y-%m-%d")
|
|
end_str = end if end else plot_df["Date"].max().strftime("%Y-%m-%d")
|
|
filename = f"bitcoin_analysis_{start_str}_to_{end_str}_with_projections.png"
|
|
plt.savefig(filename, dpi=300, bbox_inches="tight")
|
|
plt.close()
|
|
|
|
return projections
|
|
|
|
|
|
def visualize_cycle_patterns(df, cycle_returns, cycle_volatility):
|
|
"""
|
|
Create enhanced visualization of Bitcoin's behavior across halving cycles.
|
|
"""
|
|
plt.style.use("seaborn-v0_8")
|
|
fig = plt.figure(figsize=(15, 15))
|
|
|
|
# Create a 3x1 subplot grid with different heights
|
|
gs = plt.GridSpec(3, 1, height_ratios=[2, 1, 2], hspace=0.3)
|
|
|
|
# Plot 1: Returns across cycle with confidence bands
|
|
ax1 = plt.subplot(gs[0])
|
|
|
|
# Convert days to percentage through cycle
|
|
x_points = np.array(cycle_returns.index) / (4 * 365) * 100
|
|
|
|
# Calculate rolling mean and standard deviation for confidence bands
|
|
window = 30 # 30-day window
|
|
rolling_mean = pd.Series(cycle_returns.values).rolling(window=window).mean()
|
|
rolling_std = pd.Series(cycle_returns.values).rolling(window=window).std()
|
|
|
|
# Plot confidence bands
|
|
ax1.fill_between(
|
|
x_points,
|
|
(rolling_mean - 2 * rolling_std) * 100,
|
|
(rolling_mean + 2 * rolling_std) * 100,
|
|
alpha=0.2,
|
|
color="blue",
|
|
label="95% Confidence",
|
|
)
|
|
ax1.fill_between(
|
|
x_points,
|
|
(rolling_mean - rolling_std) * 100,
|
|
(rolling_mean + rolling_std) * 100,
|
|
alpha=0.3,
|
|
color="blue",
|
|
label="68% Confidence",
|
|
)
|
|
|
|
# Plot average returns
|
|
ax1.plot(
|
|
x_points,
|
|
cycle_returns.values * 100,
|
|
"b-",
|
|
label="Average Daily Return",
|
|
linewidth=2,
|
|
)
|
|
ax1.axhline(y=0, color="gray", linestyle="--", alpha=0.5)
|
|
|
|
# Add vertical lines for each year in cycle
|
|
for year in range(1, 4):
|
|
ax1.axvline(x=year * 25, color="gray", linestyle=":", alpha=0.3)
|
|
ax1.text(
|
|
year * 25,
|
|
ax1.get_ylim()[1],
|
|
f"Year {year}",
|
|
rotation=90,
|
|
va="top",
|
|
ha="right",
|
|
alpha=0.7,
|
|
)
|
|
|
|
# Highlight halving points
|
|
ax1.axvline(x=0, color="red", linestyle="--", alpha=0.5, label="Halving Event")
|
|
ax1.axvline(x=100, color="red", linestyle="--", alpha=0.5)
|
|
|
|
ax1.set_title("Bitcoin Return Patterns Across Halving Cycle", pad=20)
|
|
ax1.set_xlabel("Position in Cycle (%)")
|
|
ax1.set_ylabel("Average Daily Return (%)")
|
|
ax1.grid(True, alpha=0.3)
|
|
ax1.legend(loc="upper right")
|
|
|
|
# Plot 2: Volatility across cycle
|
|
ax2 = plt.subplot(gs[1])
|
|
|
|
# Calculate rolling volatility confidence bands
|
|
vol_mean = pd.Series(cycle_volatility.values).rolling(window=window).mean()
|
|
vol_std = pd.Series(cycle_volatility.values).rolling(window=window).std()
|
|
|
|
# Plot volatility with confidence bands
|
|
annualized_factor = np.sqrt(365) * 100
|
|
ax2.fill_between(
|
|
x_points,
|
|
(vol_mean - 2 * vol_std) * annualized_factor,
|
|
(vol_mean + 2 * vol_std) * annualized_factor,
|
|
alpha=0.2,
|
|
color="red",
|
|
label="95% Confidence",
|
|
)
|
|
ax2.plot(
|
|
x_points,
|
|
cycle_volatility.values * annualized_factor,
|
|
"r-",
|
|
label="Annualized Volatility",
|
|
linewidth=2,
|
|
)
|
|
|
|
# Add year markers
|
|
for year in range(1, 4):
|
|
ax2.axvline(x=year * 25, color="gray", linestyle=":", alpha=0.3)
|
|
|
|
ax2.axvline(x=0, color="red", linestyle="--", alpha=0.5)
|
|
ax2.axvline(x=100, color="red", linestyle="--", alpha=0.5)
|
|
|
|
ax2.set_xlabel("Position in Cycle (%)")
|
|
ax2.set_ylabel("Volatility (%)")
|
|
ax2.grid(True, alpha=0.3)
|
|
ax2.legend(loc="upper right")
|
|
|
|
# Plot 3: Average price trajectory within cycles
|
|
ax3 = plt.subplot(gs[2])
|
|
|
|
# Define a color scheme for cycles
|
|
cycle_colors = ["#1f77b4", "#ff7f0e", "#2ca02c", "#d62728", "#9467bd"]
|
|
|
|
# Calculate average price path for each cycle
|
|
halving_dates = get_halving_dates()
|
|
cycles = []
|
|
|
|
for i in range(len(halving_dates) - 1):
|
|
cycle_start = halving_dates[i]
|
|
cycle_end = halving_dates[i + 1]
|
|
cycle_data = df[(df["Date"] >= cycle_start) & (df["Date"] < cycle_end)].copy()
|
|
|
|
if len(cycle_data) > 0:
|
|
cycle_data["Cycle_Pct"] = (
|
|
(cycle_data["Date"] - cycle_start).dt.total_seconds()
|
|
/ (cycle_end - cycle_start).total_seconds()
|
|
* 100
|
|
)
|
|
cycle_data["Normalized_Price"] = (
|
|
cycle_data["Close"] / cycle_data["Close"].iloc[0]
|
|
)
|
|
cycles.append(cycle_data)
|
|
|
|
# Plot each historical cycle with distinct colors
|
|
for i, cycle in enumerate(cycles):
|
|
ax3.semilogy(
|
|
cycle["Cycle_Pct"],
|
|
cycle["Normalized_Price"],
|
|
color=cycle_colors[i],
|
|
alpha=0.7,
|
|
label=f'Cycle {i+1} ({cycle["Date"].iloc[0].strftime("%Y")}-{cycle["Date"].iloc[-1].strftime("%Y")})',
|
|
)
|
|
|
|
# Calculate and plot average cycle
|
|
if cycles:
|
|
avg_cycle = pd.concat(
|
|
[c.set_index("Cycle_Pct")["Normalized_Price"] for c in cycles], axis=1
|
|
)
|
|
avg_cycle_mean = avg_cycle.mean(axis=1)
|
|
avg_cycle_std = avg_cycle.std(axis=1)
|
|
|
|
ax3.semilogy(
|
|
avg_cycle_mean.index,
|
|
avg_cycle_mean.values,
|
|
"k-",
|
|
linewidth=2,
|
|
label="Average Cycle",
|
|
)
|
|
ax3.fill_between(
|
|
avg_cycle_mean.index,
|
|
avg_cycle_mean * np.exp(-2 * avg_cycle_std),
|
|
avg_cycle_mean * np.exp(2 * avg_cycle_std),
|
|
alpha=0.2,
|
|
color="gray",
|
|
)
|
|
|
|
# Add year markers
|
|
for year in range(1, 4):
|
|
ax3.axvline(x=year * 25, color="gray", linestyle=":", alpha=0.3)
|
|
|
|
ax3.axvline(x=0, color="red", linestyle="--", alpha=0.5)
|
|
ax3.axvline(x=100, color="red", linestyle="--", alpha=0.5)
|
|
|
|
ax3.set_title("Price Performance Across Cycles (Normalized)", pad=20)
|
|
ax3.set_xlabel("Position in Cycle (%)")
|
|
ax3.set_ylabel("Price (Relative to Cycle Start)")
|
|
ax3.grid(True, alpha=0.3)
|
|
ax3.legend(loc="center left", bbox_to_anchor=(1.02, 0.5))
|
|
|
|
# Add current cycle position marker on all plots
|
|
current_position = get_cycle_position(df["Date"].max(), halving_dates) * 100
|
|
for ax in [ax1, ax2, ax3]:
|
|
ax.axvline(
|
|
x=current_position,
|
|
color="green",
|
|
linestyle="-",
|
|
alpha=0.5,
|
|
label="Current Position",
|
|
)
|
|
|
|
# Main title for the figure
|
|
fig.suptitle("Bitcoin Halving Cycle Analysis", fontsize=16, y=0.95)
|
|
|
|
# Adjust layout to prevent legend cutoff
|
|
plt.tight_layout()
|
|
|
|
# Save the plot
|
|
plt.savefig("bitcoin_cycle_patterns.png", dpi=300, bbox_inches="tight")
|
|
plt.close()
|
|
|
|
|
|
def create_backtest_plot(
|
|
df, backtest_date="2020-05-11", start_date="2012-11-28", project_days=1650
|
|
):
|
|
"""
|
|
Create a plot comparing actual price history against model projections from a historical date.
|
|
|
|
Args:
|
|
df: DataFrame with historical price data
|
|
backtest_date: Date to start the backtest from (default: third halving)
|
|
start_date: Date to start considering historical data (default: first halving)
|
|
project_days: Number of days to project forward from backtest date
|
|
"""
|
|
# Convert dates to datetime
|
|
backtest_date = pd.to_datetime(backtest_date)
|
|
start_date = pd.to_datetime(start_date)
|
|
|
|
# Validate dates
|
|
if start_date >= backtest_date:
|
|
raise ValueError("start_date must be earlier than backtest_date")
|
|
|
|
# Clean the data: remove rows with zero or invalid prices and filter by date
|
|
df = df[(df["Close"] > 0) & (df["Date"] >= start_date)].copy()
|
|
|
|
# Split data into training (before backtest date) and validation (after backtest date)
|
|
training_df = df[df["Date"] <= backtest_date].copy()
|
|
validation_df = df[df["Date"] > backtest_date].copy()
|
|
|
|
# Check if we have enough data
|
|
if len(training_df) < 30: # Require at least 30 days of training data
|
|
raise ValueError("Insufficient training data before backtest date")
|
|
|
|
# Generate historical projections using only training data
|
|
historical_projections = project_prices(training_df, days_forward=project_days)
|
|
|
|
# Set up the plot
|
|
plt.style.use("seaborn-v0_8")
|
|
fig, ax = plt.figure(figsize=(15, 10)), plt.gca()
|
|
|
|
# Plot training data
|
|
ax.semilogy(
|
|
training_df["Date"],
|
|
training_df["Close"],
|
|
"b-",
|
|
label=f'Historical Price (Training: {start_date.strftime("%Y-%m-%d")} to {backtest_date.strftime("%Y-%m-%d")})',
|
|
alpha=0.7,
|
|
)
|
|
|
|
# Plot validation data
|
|
ax.semilogy(
|
|
validation_df["Date"],
|
|
validation_df["Close"],
|
|
"g-",
|
|
label=f'Actual Price (Validation: {backtest_date.strftime("%Y-%m-%d")} onwards)',
|
|
linewidth=2,
|
|
)
|
|
|
|
# Plot projections
|
|
ax.semilogy(
|
|
historical_projections.index,
|
|
historical_projections["Expected_Trend"],
|
|
"--",
|
|
color="purple",
|
|
label="Model Projection (Expected)",
|
|
)
|
|
ax.semilogy(
|
|
historical_projections.index,
|
|
historical_projections["Median"],
|
|
":",
|
|
color="orange",
|
|
label="Model Projection (Median)",
|
|
)
|
|
|
|
# Add confidence intervals
|
|
ax.fill_between(
|
|
historical_projections.index,
|
|
historical_projections["Lower_95"],
|
|
historical_projections["Upper_95"],
|
|
alpha=0.2,
|
|
color="orange",
|
|
label="95% Confidence Interval",
|
|
)
|
|
ax.fill_between(
|
|
historical_projections.index,
|
|
historical_projections["Lower_68"],
|
|
historical_projections["Upper_68"],
|
|
alpha=0.3,
|
|
color="green",
|
|
label="68% Confidence Interval",
|
|
)
|
|
|
|
# Customize y-axis
|
|
ax.yaxis.set_major_formatter(plt.FuncFormatter(format_price))
|
|
|
|
# Set custom y-axis ticks
|
|
min_price = min(
|
|
df["Low"].min(),
|
|
historical_projections["Lower_95"].min(),
|
|
0.0001, # Set minimum price floor
|
|
)
|
|
max_price = max(df["High"].max(), historical_projections["Upper_95"].max())
|
|
price_points = get_nice_price_points(min_price, max_price)
|
|
ax.set_yticks(price_points)
|
|
|
|
# Add halving lines
|
|
halving_dates = get_halving_dates()
|
|
relevant_halvings = halving_dates[
|
|
(halving_dates >= start_date) & (halving_dates <= validation_df["Date"].max())
|
|
]
|
|
for date in relevant_halvings:
|
|
ax.axvline(date, color="red", linestyle="--", alpha=0.3)
|
|
ax.text(
|
|
date,
|
|
ax.get_ylim()[1],
|
|
"Halving",
|
|
rotation=90,
|
|
va="top",
|
|
ha="right",
|
|
alpha=0.7,
|
|
)
|
|
|
|
# Calculate and add model performance metrics
|
|
if len(validation_df) > 0:
|
|
# Create a common date range for comparison
|
|
actual_prices = validation_df.set_index("Date")["Close"]
|
|
common_dates = actual_prices.index.intersection(historical_projections.index)
|
|
|
|
if len(common_dates) > 0:
|
|
actual_aligned = actual_prices[common_dates]
|
|
projections_aligned = historical_projections.loc[common_dates]
|
|
|
|
# Calculate metrics using aligned data
|
|
mape = (
|
|
np.mean(
|
|
np.abs(
|
|
(actual_aligned - projections_aligned["Expected_Trend"])
|
|
/ actual_aligned
|
|
)
|
|
)
|
|
* 100
|
|
)
|
|
coverage_95 = (
|
|
np.mean(
|
|
(actual_aligned >= projections_aligned["Lower_95"])
|
|
& (actual_aligned <= projections_aligned["Upper_95"])
|
|
)
|
|
* 100
|
|
)
|
|
coverage_68 = (
|
|
np.mean(
|
|
(actual_aligned >= projections_aligned["Lower_68"])
|
|
& (actual_aligned <= projections_aligned["Upper_68"])
|
|
)
|
|
* 100
|
|
)
|
|
rmse = np.sqrt(
|
|
np.mean((actual_aligned - projections_aligned["Expected_Trend"]) ** 2)
|
|
)
|
|
max_error = np.max(
|
|
np.abs(actual_aligned - projections_aligned["Expected_Trend"])
|
|
)
|
|
|
|
# Add metrics to plot
|
|
metrics_text = (
|
|
f"Model Performance Metrics:\n"
|
|
f"MAPE: {mape:.1f}%\n"
|
|
f"RMSE: ${rmse:,.0f}\n"
|
|
f"Max Error: ${max_error:,.0f}\n"
|
|
f"95% CI Coverage: {coverage_95:.1f}%\n"
|
|
f"68% CI Coverage: {coverage_68:.1f}%"
|
|
)
|
|
ax.text(
|
|
0.02,
|
|
0.98,
|
|
metrics_text,
|
|
transform=ax.transAxes,
|
|
verticalalignment="top",
|
|
bbox=dict(facecolor="white", alpha=0.8),
|
|
)
|
|
|
|
# Customize plot
|
|
ax.set_title(
|
|
f'Bitcoin Price: Model Backtest\nTraining: {start_date.strftime("%Y-%m-%d")} to {backtest_date.strftime("%Y-%m-%d")}'
|
|
)
|
|
ax.set_xlabel("Date")
|
|
ax.set_ylabel("Price (USD)")
|
|
ax.grid(True, which="major", linestyle="-", alpha=0.5)
|
|
ax.grid(True, which="minor", linestyle=":", alpha=0.2)
|
|
ax.legend(loc="center left", bbox_to_anchor=(1.02, 0.5))
|
|
|
|
# Adjust layout and save
|
|
plt.tight_layout()
|
|
filename = f'bitcoin_backtest_{start_date.strftime("%Y%m%d")}_to_{backtest_date.strftime("%Y%m%d")}.png'
|
|
plt.savefig(filename, dpi=300, bbox_inches="tight")
|
|
plt.close()
|
|
|
|
return historical_projections
|
|
|
|
|
|
if __name__ == "__main__":
|
|
analysis, df = analyze_bitcoin_prices("prices.csv")
|
|
# create_plots(df) # Full history
|
|
# create_plots(df, start='2022-01-01') # From 2022 onwards
|
|
# create_plots(df, start='2023-01-01', end='2023-12-31') # Just 2023
|
|
# Create plots with different time ranges and projections
|
|
projections = create_plots(df, start="2011-01-01", project_days=365 * 4)
|
|
print("\nProjected Prices at Key Points:")
|
|
print(projections.iloc[[29, 89, 179, 364]].round(2)) # 30, 90, 180, 365 days
|
|
|
|
# Create multiple backtests for different periods
|
|
backtests = [
|
|
# First to second halving
|
|
{
|
|
"start_date": "2012-11-28", # First halving
|
|
"backtest_date": "2016-07-09", # Second halving
|
|
"project_days": 1460, # 4 years
|
|
},
|
|
# Second to third halving
|
|
{
|
|
"start_date": "2016-07-09", # Second halving
|
|
"backtest_date": "2020-05-11", # Third halving
|
|
"project_days": 1460, # 4 years
|
|
},
|
|
# Third halving onwards
|
|
{
|
|
"start_date": "2020-05-11", # Third halving
|
|
"backtest_date": "2024-04-19", # Fourth halving (projected)
|
|
"project_days": 1460, # 4 years
|
|
},
|
|
{
|
|
"start_date": "2016-07-09", # Second halving
|
|
"backtest_date": "2024-04-19", # Fourth halving (projected)
|
|
"project_days": 1460, # 4 years
|
|
},
|
|
]
|
|
|
|
# Run all backtests
|
|
for params in backtests:
|
|
print(
|
|
f"\nRunning backtest from {params['start_date']} to {params['backtest_date']}"
|
|
)
|
|
backtest_projections = create_backtest_plot(df, **params)
|
|
|
|
# Print some key projection points vs actual prices
|
|
print("\nBacktest Results - Projected vs Actual Prices:")
|
|
validation_df = df[df["Date"] > params["backtest_date"]]
|
|
actual_prices = validation_df.set_index("Date")["Close"]
|
|
|
|
for days in [30, 90, 180, 365]:
|
|
target_date = pd.to_datetime(params["backtest_date"]) + pd.Timedelta(
|
|
days=days
|
|
)
|
|
if (
|
|
target_date in actual_prices.index
|
|
and target_date in backtest_projections.index
|
|
):
|
|
projected = backtest_projections.loc[target_date]
|
|
actual = actual_prices.loc[target_date]
|
|
print(f"\n{days} days out ({target_date.strftime('%Y-%m-%d')}):")
|
|
print(f"Actual Price: ${actual:,.2f}")
|
|
print(f"Projected (Expected): ${projected['Expected_Trend']:,.2f}")
|
|
print(
|
|
f"Projected Range: ${projected['Lower_95']:,.2f} - ${projected['Upper_95']:,.2f}"
|
|
)
|