MIDASVAR.fit

MIDASVAR.fit()

Estimate the system by profiled maximum likelihood.

Conditional on the polynomial parameters the model is linear, so the inner problem is one least-squares solve with the covariance concentrated out; the outer search is derivative-free over the two parameters per high-frequency series, multi-started because the decay direction can be multi-modal.

Return type:

MIDASVARResult

Returns:

The fitted result.

Example

>>> import numpy as np
>>> rng = np.random.default_rng(0)
>>> x = rng.standard_normal((360, 1))
>>> window = 0.7 * x[2::3, 0] + 0.3 * x[1::3, 0]
>>> noise = 0.1 * rng.standard_normal(120)
>>> y = np.column_stack([window + noise, rng.standard_normal(120)])
>>> res = MIDASVAR(y, x, order=1, period=3).fit()
>>> res.theta.shape, res.exog.shape, res.design.shape
((1, 2), (119, 1), (119, 4))
>>> bool(np.allclose(res.design[:, -1:], res.exog))
True