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