CUSUM Tests

cusum_test_step(
    name: str,
    *,
    y_source: InpSources,
    x_source: InpSources,
    filter_key: str = "filter",
    payload_key: str | None = None,
    y_column: Sequence[int] | int | None = None,
    X_columns: Sequence[int] | slice | None = None,
    burn_in: int = 0,
    drop_initial: bool = False,
    alpha: float = 0.05,
) -> MCStep

cusum_test_step wraps run_cusum_test(...). It resolves a single response column from y_source and a regressor matrix from x_source, then tests the regression coefficients for stability using the cumulative sum of standardized recursive (Brown-Durbin-Evans) residuals.

Reference Distribution

The test is parameter-free: the boundary-crossing probability is Durbin's closed-form approximation evaluated directly on the statistic, so the reported degrees of freedom are not applicable (rendered as N/A).

Response must be 1D

y_source must resolve to exactly one column, and the response 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].