CUSUM of Squares Tests

cusumsq_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

cusumsq_test_step wraps run_cusumsq_test(...). It resolves a single response column from y_source and a regressor matrix from x_source, then tests the regression variance for stability using the cumulative sum of squared recursive (Brown-Durbin-Evans) residuals. Where the CUSUM test targets shifts in the coefficients, the CUSUM of squares targets shifts in the residual variance.

Reference Distribution

The statistic is the maximum departure of the normalized squared-residual partial sums from their expected line, compared against a Kolmogorov-type survival function parameterized by the recursive-residual count \(n = T - p\) (reported as the degrees of freedom).

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].