TVPVAR#

class cultivars.multivariate.nonlinear.time_varying.TVPVAR(endog, *, order, training=None, trend='c', names=None)[source]#

Time-varying-parameter VAR with constant innovation covariance.

The stacked coefficient vector follows a random walk, \(\beta_t = \beta_{t-1} + \eta_t\) with \(\eta_t \sim N(0, Q)\), and the innovations are homoskedastic, \(u_t \sim N(0, \Sigma)\). The priors come from a training sample split off the front: its OLS estimate \(\hat b_0\) and covariance \(\hat V_0\) give the initial state \(\beta_0 \sim N(\hat b_0, 4 \hat V_0)\), the drift covariance an inverse-Wishart prior with scale \(k_Q^2\,\nu_Q\,\hat V_0\) and \(\nu_Q = \max(\tau, D + 2)\) degrees of freedom, and \(\Sigma\) an inverse-Wishart prior centred on the training covariance with \(k + 2\) degrees of freedom. The training rows are then discarded.

Variables:

  • _endog – The observed panel, from the base model.

  • _order – The autoregressive order p, from the base model.

  • _trend – The deterministic specification, from the base model.

  • _names – The variable labels, from the base model.

  • _prior – The base slot, unused: the priors here come from the training sample.

  • _training – The resolved training-sample length.

Parameters:

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

  • order (int) – Autoregressive order.

  • training (int | None) – Rows split off the front to calibrate the priors, then discarded. Defaults to roughly forty, floored by what the prior regression needs.

  • trend (Literal['n', 'c', 'ct']) – Deterministic terms.

  • names (Sequence[str] | None) – One label per variable. Defaults to y1 ... yk.

Raises:

  • SpecificationError – If the specification is malformed or the training sample is shorter than w + k + 2 rows, the floor at which the prior regression is identified.

  • DimensionError – If fewer than 2 w estimation rows remain after the training split.

See also

  • TVPVARResult – the record fit returns.

  • TVPVARSV – the same drift with stochastic volatility.

  • BVAR – the constant-coefficient conjugate model.

References

Cogley, T., & Sargent, T. J. (2005). Drifts and volatilities: Monetary policies and outcomes in the post WWII US. Review of Economic Dynamics, 8(2), 262-302.

Primiceri, G. E. (2005). Time varying structural vector autoregressions and monetary policy. Review of Economic Studies, 72(3), 821-852.

Example

>>> import numpy as np
>>> rng = np.random.default_rng(0)
>>> y = np.zeros((140, 2))
>>> for t in range(1, 140):
...     a = 0.4 + 0.3 * t / 140
...     y[t] = a * y[t - 1] + rng.standard_normal(2)
>>> res = TVPVAR(y, order=1, training=40).fit(n_draws=40, n_burn=15, seed=0)
>>> res.coefficient_path("y1", "y1.L1").shape
(99, 3)
>>> TVPVAR(y, order=1).training, TVPVAR(y, order=2, training=20).training
(40, 20)
>>> TVPVAR(y, order=1, training=4)
Traceback (most recent call last):
cultivars.exceptions.SpecificationError: a training sample of 4 rows cannot identify ...

Attributes#

endog

The validated sample.

is_shrunk

Whether a prior contributes anything to this estimate.

k_endog

Number of endogenous variables.

n_regressors

Regressors per equation.

names

Variable labels.

order

Autoregressive order.

prior

The prior on the coefficients; NoPrior when unrestricted.

training

Rows consumed by the training prior.

trend

Deterministic specification.

Methods#

fit(*[, n_draws, n_burn, thin, k_drift, seed])

Estimate by Gibbs sampling.

lag_order_selection([max_lags])

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