MIDASVAR#

class cultivars.multivariate.reduced_form.mixed_frequency.MIDASVAR(endog, exog_high, *, order, period, midas_lags=None, trend='c', names=None, exog_names=None)[source]#

A low-frequency VAR reading high-frequency data through a lag polynomial.

The model is \(y_t = D d_t + A_1 y_{t-1} + \dots + A_p y_{t-p} + B\, x_t(\theta) + u_t\) at the low frequency, where \(x_t(\theta)\) compresses the last midas_lags sub-period readings of each high-frequency series into one number with normalized exponential-Almon weights \(w_j \propto \exp(\theta_1 j + \theta_2 j^2)\). Two parameters per series buy the whole within-period history, which is the entire point of MIDAS: the unrestricted alternative spends midas_lags coefficients per series per equation and eats the sample.

This class estimates, unlike its state-space sibling, because nothing here is temporally aggregated: every regressor is observed, the model is linear conditional on the polynomial, and the likelihood identifies everything it touches. Estimation profiles the polynomial – an inner least-squares solve conditional on theta, an outer derivative-free search over it, multi-started because the decay direction can be multi-modal. Lag-order selection holds the weights flat so that the candidates differ in the endogenous order and in nothing else.

Variables:

  • _endog – The validated (nobs, k) low-frequency panel.

  • _names – Endogenous labels.

  • _order – Endogenous autoregressive order.

  • _trend – Deterministic terms.

  • _prior – The base slot for a shrinkage prior, unused by this family.

  • _exog_high – The validated (nobs * period, m) high-frequency panel.

  • _exog_names – High-frequency labels.

  • _period – Sub-periods per low-frequency period.

  • _midas_lags – Sub-periods each weight curve spans.

See also

  • MIDASVARResult – the record fit() returns.

  • MFVAR – the high-frequency model, which infers a latent path from supplied parameters instead of estimating.

  • VARX – the right model when period would be one.

References

Ghysels, E., Santa-Clara, P., & Valkanov, R. (2004). The MIDAS touch: Mixed data sampling regression models. CIRANO Working Paper 2004s-20.

Ghysels, E., Sinko, A., & Valkanov, R. (2007). MIDAS regressions: Further results and new directions. Econometric Reviews, 26(1), 53-90.

Example

>>> import numpy as np
>>> rng = np.random.default_rng(0)
>>> x = rng.standard_normal((120, 1))
>>> y = np.column_stack(
...     [x[2::3, 0] + 0.1 * rng.standard_normal(40), rng.standard_normal(40)]
... )
>>> res = MIDASVAR(y, x, order=1, period=3).fit()
>>> res.forecast(2, exog_high_future=np.zeros((6, 1))).shape
(2, 2)

Attributes#

endog

The validated sample.

exog_high

The validated high-frequency panel.

exog_names

High-frequency labels.

is_shrunk

Whether a prior contributes anything to this estimate.

k_endog

Number of endogenous variables.

k_exog

Number of high-frequency series.

midas_lags

Sub-periods each weight curve spans.

n_regressors

Regressors per equation, including the compressed block.

names

Variable labels.

order

Autoregressive order.

period

Sub-periods per low-frequency period.

prior

The prior on the coefficients; NoPrior when unrestricted.

trend

Deterministic specification.

Methods#

fit()

Estimate the system by profiled maximum likelihood.

lag_order_selection([max_lags])

Score every order from zero to max_lags on one common sample.
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