VarBayes

model.VarBayes(
    self,
    data,
    lag=1,
    n_chain=1,
    n_iter=1000,
    n_burn=None,
    n_thin=1,
    bayes_config=SsvsConfig(),
    cov_config=LdltConfig(),
    intercept_config=InterceptConfig(),
    fit_intercept=True,
    minnesota=True,
    verbose=False,
    n_thread=1,
)

Bayesian Vector Autoregressive Model

Fits Bayesian VAR model.

Parameters

Name	Type	Description	Default
data	array - like	Time series data of which columns indicate the variables	required
lag	int	VAR lag, by default 1	`1`
n_chain	int	Number of MCMC chains, by default 1	`1`
n_iter	int	Number of MCMC total iterations, by default 1000	`1000`
n_burn	int	MCMC burn-in (warm-up), by default `floor(n_iter / 2)`	`None`
n_thin	int	Thinning every `n_thin`-th iteration, by default 1	`1`
bayes_config	_BayesConfig	Prior configuration, by default SsvsConfig()	`SsvsConfig()`
cov_config	(LdltConfig, SvConfig)	Prior configuration for covariance matrix, by default LdltConfig()	`'LdltConfig'`
intercept_config	InterceptConfig	Prior configuration for constant term, by default InterceptConfig()	`InterceptConfig()`
fit_intercept	bool	Include constant term in the model, by default True	`True`
minnesota	bool	If `True`, apply Minnesota-type group structure, by default True	`True`
verbose	bool	If `True`, print progress bar for MCMC, by default False	`False`
n_thread	int	Number of OpenMP threads, by default 1	`1`

Attributes

Name	Type	Description
coef_	ndarray	VHAR coefficient matrix.
intercept_	ndarray	VHAR model constant vector.
n_features_in_	int	Number of variables.

References

.. [1] Carriero, A., Chan, J., Clark, T. E., & Marcellino, M. (2022). Corrigendum to “Large Bayesian vector autoregressions with stochastic volatility and non-conjugate priors” [J. Econometrics 212 (1)(2019) 137–154]. Journal of Econometrics, 227(2), 506-512. .. [2] Chan, J., Koop, G., Poirier, D., & Tobias, J. (2019). Bayesian Econometric Methods (2nd ed., Econometric Exercises). Cambridge: Cambridge University Press. .. [3] 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. .. [4] Gruber, L., & Kastner, G. (2022). Forecasting macroeconomic data with Bayesian VARs: Sparse or dense? It depends! arXiv. .. [5] Huber, F., Koop, G., & Onorante, L. (2021). Inducing Sparsity and Shrinkage in Time-Varying Parameter Models. Journal of Business & Economic Statistics, 39(3), 669–683. .. [6] Korobilis, D., & Shimizu, K. (2022). Bayesian Approaches to Shrinkage and Sparse Estimation. Foundations and Trends® in Econometrics, 11(4), 230–354. .. [7] Ray, P., & Bhattacharya, A. (2018). Signal Adaptive Variable Selector for the Horseshoe Prior. arXiv.

Methods

Name	Description
expand_forecast	Expanding-window forecasting
fit	Conduct MCMC and compute posterior mean
predict	‘n_ahead’-step ahead forecasting
roll_forecast	Rolling-window forecasting

expand_forecast

model.VarBayes.expand_forecast(
    n_ahead,
    test,
    level=0.05,
    stable=False,
    sparse=False,
    med=False,
    sv=True,
)

Expanding-window forecasting

Parameters

Name	Type	Description	Default
n_ahead	int	Forecast next `n_ahead` time point.	required
test	array - like	Test set to forecast	required
level	float	Level for credible interval, by default .05	`0.05`
stable	bool	Filter stable coefficient draws, by default True	`False`
sparse	bool	Apply restriction to forecasting, by default False	`False`
med	bool	Use median instead of mean to get point forecast, by default False	`False`
sv	bool	Use SV term in case of SV model, by default True	`True`

Returns

Name	Type	Description
	dict	Density forecasting results - “forecast” (ndarray): Posterior mean of forecasting - “se” (ndarray): Standard error of forecasting - “lower” (ndarray): Lower quantile of forecasting - “upper” (ndarray): Upper quantile of forecasting - “lpl” (float): Average log-predictive likelihood

fit

model.VarBayes.fit()

Conduct MCMC and compute posterior mean

Returns

Name	Type	Description
self	object	An instance of the estimator.

predict

model.VarBayes.predict(
    n_ahead,
    level=0.05,
    stable=False,
    sparse=False,
    med=False,
    sv=True,
)

‘n_ahead’-step ahead forecasting

Parameters

Name	Type	Description	Default
n_ahead	int	Forecast until next `n_ahead` time point.	required
level	float	Level for credible interval, by default .05	`0.05`
stable	bool	Filter stable coefficient draws, by default True	`False`
sparse	bool	Apply restriction to forecasting, by default False	`False`
med	bool	Use median instead of mean to get point forecast, by default False	`False`
sv	bool	Use SV term in case of SV model, by default True	`True`

Returns

Name	Type	Description
	dict	Density forecasting results - “forecast” (ndarray): Posterior mean of forecasting - “se” (ndarray): Standard error of forecasting - “lower” (ndarray): Lower quantile of forecasting - “upper” (ndarray): Upper quantile of forecasting

roll_forecast

model.VarBayes.roll_forecast(
    n_ahead,
    test,
    level=0.05,
    stable=False,
    sparse=False,
    med=False,
    sv=True,
)

Rolling-window forecasting

Parameters

Name	Type	Description	Default
n_ahead	int	Forecast next `n_ahead` time point.	required
test	array - like	Test set to forecast	required
level	float	Level for credible interval, by default .05	`0.05`
stable	bool	Filter stable coefficient draws, by default True	`False`
sparse	bool	Apply restriction to forecasting, by default False	`False`
med	bool	Use median instead of mean to get point forecast, by default False	`False`
sv	bool	Use SV term in case of SV model, by default True	`True`

Returns

Name	Type	Description
	dict	Density forecasting results - “forecast” (ndarray): Posterior mean of forecasting - “se” (ndarray): Standard error of forecasting - “lower” (ndarray): Lower quantile of forecasting - “upper” (ndarray): Upper quantile of forecasting - “lpl” (float): Average log-predictive likelihood