Information Discreteness

Intuição

A Information Discreteness (Da, Gurun & Warachka) tenta capturar se a informação chega via muitos pequenos movimentos (mais “contínuo”) ou poucos grandes movimentos (mais “discreto”).

Definição

Em uma janela n:

• r_total = sum(r_i)
• s_total = sign(r_total)
• ID = s_total * ( %dias com sign(r_i)=s_total - %dias com sign(r_i)=-s_total )

O output fica em [-1, 1].

Uso

from quantmaster.features.statistical import information_discreteness

df["id_20"] = information_discreteness(df, window=20)

API

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

def information_discreteness(
    data: pd.DataFrame | pd.Series,
    *,
    window: int = 20,
    price_col: str = "close",
    log_returns: bool = True,
) -> pd.Series:
    window = validate_positive_int(window, name="window")

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

    if log_returns:
        rets = np.log(price).diff()
    else:
        rets = price.pct_change()

    out = pd.Series(np.nan, index=price.index, dtype=float)
    out.name = f"information_discreteness_{window}"

    if len(rets) < window:
        return out

    r = rets.to_numpy(dtype=float)
    rw = np.lib.stride_tricks.sliding_window_view(r, window_shape=window)

    id_arr = np.full(rw.shape[0], np.nan, dtype=float)
    for i in range(rw.shape[0]):
        w = rw[i]
        w = w[np.isfinite(w)]
        if w.size < 2:
            continue

        r_total = float(np.sum(w))
        s_total = float(np.sign(r_total))
        if s_total == 0.0:
            id_arr[i] = 0.0
            continue

        s = np.sign(w)
        s = s[s != 0.0]
        if s.size == 0:
            continue

        same = float(np.mean(s == s_total))
        opp = float(np.mean(s == -s_total))
        id_arr[i] = s_total * (same - opp)

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