Breusch-Pagan Tests

breusch_pagan_test_step(
    name: str,
    *,
    residual_source: InpSources,
    X_source: InpSources,
    filter_key: str = "filter",
    residual_payload_key: str | None = None,
    x_payload_key: str | None = None,
    residual_col: Sequence[int] | int | None = None,
    X_columns: Sequence[int] | slice | None = None,
    burn_in: int = 0,
    drop_initial: bool = False,
    alpha: float = 0.05,
    robust: bool = False,
) -> MCStep

breusch_pagan_test_step wraps run_breusch_pagan_test(...). It resolves a single residual column from residual_source and a regressor matrix from X_source, then tests the residuals for heteroskedasticity by regressing their squares on the regressors.

Reference Distribution

The Lagrange-multiplier statistic is compared against a \(\chi^2(p)\) distribution, where \(p\) is the number of regressor columns. Set robust=True for Koenker's studentized variant, which is robust to non-normal residuals.

Residuals must be 1D

residual_source must resolve to exactly one column, and the residual and regressor arrays must share the same number of rows.

Sources:

Source	Description
states	Use context.data.states. Set drop_initial=True to remove the initial state row.
observables	Use context.data.observables.
x_pred, x_filt, y_pred, y_filt, innov, std_innov	Read arrays from the FilterResult stored under filter_key.
payload	Read an array-like object from context.payloads[payload_key].