ssfortran.diagnostics.ljung_box

ssfortran.diagnostics.ljung_box(x, lags=10, model_df=0)

Test for serial correlation with the Ljung-Box statistic.

\(Q(k) = n (n + 2) \sum_{j=1}^k \rho_j^2 / (n - j)\), referred to \(\chi^2\) with k - model_df degrees of freedom (DK §2.12.1).

Parameters:

xarray_like

Residuals.

lagsint, optional

Largest lag k.

model_dfint, optional

Degrees of freedom to subtract, e.g. the number of ARMA coefficients.

Returns:

statndarray, shape (lags,)

\(Q(1), \dots, Q(k)\).

pvaluendarray, shape (lags,)

Their p-values.

Notes

Pairs with a NaN are skipped, and n is the number of non-NaN values.

Examples

>>> e = np.random.default_rng(0).standard_normal(200)
>>> stat, pvalue = ss.diagnostics.ljung_box(e, lags=5)
>>> stat.shape
(5,)