LongMemorySVResult.quasi_state_space#

LongMemorySVResult.quasi_state_space(truncation=100)[source]#

The linearized model as a truncated AR(inf) linear-Gaussian state space.

The fractional operator has no finite state, so this is the autoregressive representation cut at truncation lags on the log-squared data: exact for the truncated law, an approximation of the long-memory one, and the pi**2 / 2 measurement floor is the linearization’s. What the Kalman filter returns on it is a truncated quasi-likelihood, not the model’s likelihood.

Parameters:

truncation (int) – Autoregressive lags retained, at least 1.

Return type:

_LinearGaussianStateSpace

Returns:

The linear-Gaussian state-space model in the log-squared data.

Raises:

SpecificationError – If truncation is not positive.

Example

>>> import numpy as np
>>> rng = np.random.default_rng(0)
>>> res = LongMemorySV(rng.standard_normal(300), mean="zero").fit()
>>> system = res.quasi_state_space(20)
>>> type(system).__name__, system.k_states, system.k_endog
('_LinearGaussianStateSpace', 20, 1)
>>> res.quasi_state_space(0)
Traceback (most recent call last):
cultivars.exceptions.SpecificationError: truncation must be at least 1; got 0.