Generalized Hurst Exponent

Intuição

O Generalized Hurst Exponent (GHE) generaliza o Hurst para diferentes ordens de momentos (q), capturando propriedades multi-escala e memória longa.

Definição

Para lags tau = 1..max_lag, compute:

K_q(tau) = E(|X(t+tau) - X(t)|^q)

Ajuste uma regressão em log-log:

log(K_q(tau)) = a + (q*H(q)) * log(tau)

Então:

H(q) = slope / q

Uso

from quantmaster.features.statistical import generalized_hurst_exponent

df["ghe"] = generalized_hurst_exponent(df, window=100, q=2.0, max_lag=10)

API

Source code in src/quantmaster/features/statistical.py

def generalized_hurst_exponent(
    data: pd.DataFrame | pd.Series,
    *,
    window: int = 100,
    q: float = 2.0,
    max_lag: int = 20,
    price_col: str = "close",
) -> pd.Series:
    window = validate_positive_int(window, name="window")
    max_lag = validate_positive_int(max_lag, name="max_lag")
    try:
        q = float(q)
    except (TypeError, ValueError) as exc:
        raise TypeError(f"q must be float, got {type(q).__name__}") from exc
    if q <= 0:
        raise ValueError(f"q must be > 0, got {q}")
    if max_lag >= window:
        raise ValueError(f"max_lag must be < window, got max_lag={max_lag} window={window}")

    price = get_price_series(data, price_col=price_col).astype(float)
    price = price.where(price > 0)
    x = np.log(price)

    out = pd.Series(np.nan, index=price.index, dtype=float)
    out.name = f"generalized_hurst_exponent_{window}_{q:g}_{max_lag}"

    if len(x) < window:
        return out

    arr = x.to_numpy(dtype=float)
    windows = np.lib.stride_tricks.sliding_window_view(arr, window_shape=window)
    vals = np.full(windows.shape[0], np.nan, dtype=float)
    for i in range(windows.shape[0]):
        vals[i] = _generalized_hurst_exponent_1d(windows[i], q=q, max_lag=max_lag)

    out.iloc[window - 1 :] = vals
    return out