VARX#

class cultivars.multivariate.reduced_form.vector_autoregression.VARX(endog, exog, *, order, exog_order=0, trend='c', names=None, exog_names=None)[source]#

Vector autoregression with exogenous regressors, estimated by least squares.

The design gains one (m,) block per exogenous lag, placed after the endogenous lags so that every offset the base computes stays correct without an override. The constructor is inherited from _ExogenousVectorAutoRegressionModel; the exogenous sample must be aligned with the endogenous one row for row and the two label sets may not overlap. No prior is accepted here.

Parameters:

  • endog (ArrayLike) – The (nobs, k) endogenous panel.

  • exog (ArrayLike) – The (nobs, m) exogenous block, aligned on the same index.

  • order (int) – Endogenous autoregressive order p.

  • exog_order (int) – Exogenous lags s beyond the contemporaneous term. Defaults to zero.

  • trend (Literal['n', 'c', 'ct']) – "n", "c" (default) or "ct".

  • names (Sequence[str] | None) – Endogenous labels. Defaults to y1 ... yk.

  • exog_names (Sequence[str] | None) – Exogenous labels. Defaults to x1 ... xm.

Raises:

  • SpecificationError – If exog_order is malformed, the labels are malformed, or an endogenous and an exogenous label collide.

  • DimensionError – If the two samples are not aligned or the sample is too short for the specification.

Variables:

  • _endog – The validated (nobs, k) endogenous panel.

  • _exog – The validated (nobs, m) exogenous block.

  • _names – The resolved endogenous labels.

  • _exog_names – The resolved exogenous labels.

  • _order – The endogenous order.

  • _exog_order – The exogenous order.

  • _trend – The validated trend code.

  • _prior – Always _NoPrior.

See also

  • VARXResult – the record fit() returns.

  • VAR – the model without the exogenous block.

  • VECMX – the exogenous block under a cointegration restriction.

Example

>>> import numpy as np
>>> rng = np.random.default_rng(0)
>>> x = rng.standard_normal((200, 1))
>>> y = np.column_stack([x[:, 0] + rng.standard_normal(200), rng.standard_normal(200)])
>>> res = VARX(y, x, order=1, exog_order=1).fit()
>>> res.forecast(3, exog_future=np.zeros((3, 1))).shape
(3, 2)
>>> VARX(y, x, order=1, names=("a", "b"), exog_names=("a",))
Traceback (most recent call last):
cultivars.exceptions.SpecificationError: names and exog_names must not overlap, ...

Attributes#

endog

The validated sample.

exog

The validated exogenous block.

exog_names

Exogenous labels.

exog_order

Exogenous lags beyond the contemporaneous term.

is_shrunk

Whether a prior contributes anything to this estimate.

k_endog

Number of endogenous variables.

k_exog

Number of exogenous variables.

n_regressors

Regressors per equation, including the distributed lag.

names

Variable labels.

order

Autoregressive order.

prior

The prior on the coefficients; NoPrior when unrestricted.

trend

Deterministic specification.

Methods#

fit()

Estimate the system and return the fitted result.

lag_order_selection([max_lags])

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