"""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