arch.bootstrap.StepM¶

StepM multiple comparison procedure of Romano and Wolf.

Parameters:¶

benchmark: ndarray | DataFrame | Series¶: T element array of benchmark model losses
models: ndarray | DataFrame | Series¶: T by k element array of alternative model losses
size: float = 0.05¶: Value in (0,1) to use as the test size when implementing the comparison. Default value is 0.05.
block_size: int | None = None¶: Length of window to use in the bootstrap. If not provided, sqrt(T) is used. In general, this should be provided and chosen to be appropriate for the data.
reps: int = 1000¶: Number of bootstrap replications to uses. Default is 1000.
bootstrap: 'stationary' | 'sb' | 'circular' | 'cbb' | 'moving block' | 'mbb' = 'stationary'¶: Bootstrap to use. Options are ‘stationary’ or ‘sb’: Stationary bootstrap (Default) ‘circular’ or ‘cbb’: Circular block bootstrap ‘moving block’ or ‘mbb’: Moving block bootstrap
studentize: bool = True¶: Flag indicating to studentize loss differentials. Default is True
nested: bool = False¶: Flag indicating to use a nested bootstrap to compute variances for studentization. Default is False. Note that this can be slow since the procedure requires k extra bootstraps.
seed: int | Generator | RandomState | None = None¶: Seed value to use when creating the bootstrap used in the comparison. If an integer or None, the NumPy default_rng is used with the seed value. If a Generator or a RandomState, the argument is used.

Notes

The size controls the Family Wise Error Rate (FWER) since this is a multiple comparison procedure. Uses SPA and the consistent selection procedure.

See [1] for detail.

`compute`()	Compute the set of superior models.
`reset`()	Reset the bootstrap to it's initial state.