Till Örebro universitet

This paper is motivated by the findings of our previous work, that is forecasting VAR models in the cases of small and medium-sized datasets, both marginalized marginal likelihood and predictive likelihood based averaging approaches tend to produce superior forecasts than the Bayesian VAR methods using shrinkage priors. With an efficient reversible-jump MCMC algorithm, We extend the forecast combination and model averaging of VAR models to the context of large datasets (more than hundred predictors), and consider a range of competitive alternative methods to compare and examine their forecast performance. Our empirical results show that the Bayesian model averaging approach outperforms the various alternatives.

Reduced rank regression has a long tradition as a technique to achieve a parsimonious parameterization in multivariate regression models. Recently this has been applied in the Bayesian VAR framework where the rich parameterization is a common concern in applied work. We advocate a parameterization of the reduced rank VAR which leads to a natural interpretation in terms of a dynamic factor model. Without additional restrictions on the parameters the reduced rank model is unidentified and we consider two identification schemes. The traditional ad-hoc identification with the first rows of one of the reduced rank parameter matrices being the identity matrix and a semi-orthogonal identification originally proposed in the context of cointegrated VAR models with the advantage that it does not depend on the ordering of the variables. Borrowing from the cointegration literature, we propose efficient MCMC algorithms for the evaluation of the posterior distribution given the two identification schemes. The determination of the rank of the reduced rank VAR is an important practical issue and we study the performance of different criteria for determining the rank. Finally, the forecasting performance of the reduced rank VAR model is evaluated in comparison with other popular forecasting models for large data sets.

Most studies estimate the VAR models with equal lag length. Little attention has been paid to the issue of lag specifications. In this paper we propose VAR models with asymmetric lags via Bayesian sparse learning. Three popular sparse priors, L1-penalized Lasso, the mixture of L1 and L2 penalties elastic net, and spike and slab type are developed using hierarchical Bayes formulation. The model identification performance is assessed with Monte Carlo experiment and the forecasting performance is evaluated with US macroeconomic data.

Bayesian model averaging and model selection is based on the marginal likelihoods of the competing models. This can, however, not be used directly in VAR models when one of the issues is which - and how many - variables to include in the model since the likelihoods will be for different groups of variables and not directly comparable. One possible solution is to consider the marginal likelihood for a core subset of variables that are always included in the model. This is similar in spirit to a recent proposal for forecast combination based on the predictive likelihood. The two approaches are contrasted and their performance is evaluated in a simulation study and a forecasting exercise.