Wald Tests

wald_test_step(
    name: str,
    *,
    source: Literal[
        "states",
        "observables",
        "x_pred",
        "x_filt",
        "y_pred",
        "y_filt",
        "innov",
        "std_innov",
        "payload",
    ],
    target: ndarray,
    kind: Literal["mean", "covariance", "second_moment"] = "mean",
    filter_key: str = "filter",
    payload_key: str | None = None,
    columns: Sequence[int] | slice | None = None,
    burn_in: int = 0,
    drop_initial: bool = False,
    kernel: Literal["bartlett", "parzen", "qs"] = "bartlett",
    bandwidth: int | Literal["andrews", "wooldridge", "auto"] | None = "auto",
    alpha: float = 0.05,
) -> MCStep

wald_test_step wraps run_wald_test(...). It selects a 1D or 2D array from generated data, a FilterResult, or a named payload, then runs the requested HAC Wald diagnostic.

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].

Kinds:

Kind	Description
mean	Tests E[g_t] = target.
covariance	Tests the vech representation of the covariance matrix against target.
second_moment	Tests the vech representation of the raw second moment against target.