UnobservedComponentsResult.irregular

property UnobservedComponentsResult.irregular: NDArray[float64]

The observed series minus the smoothed signal, shape (n,).

The smoothed estimate of \(\varepsilon_t\); its sample variance is below sigma2_irregular because smoothing shrinks the estimate toward zero.

Example

>>> import numpy as np
>>> rng = np.random.default_rng(0)
>>> y = np.cumsum(0.2 * rng.standard_normal(200)) + rng.standard_normal(200)
>>> res = UnobservedComponents(y).fit()
>>> bool(np.allclose(res.signal + res.irregular, y))
True
>>> bool(res.irregular.var() < res.sigma2_irregular)
True