Title: Comparison of Bayesian models in the context of recursive density predictions on the example of VEC-SV-GARCH models
Authors: Anna Pajor - Cracow University of Economics (Poland)
Jacek Osiewalski - Cracow University of Economics (Poland)
Justyna Wroblewska - Cracow University of Economics (Poland)
Lukasz Kwiatkowski - Cracow University of Economics (Poland) [presenting]
Abstract: The focus is on a formal Bayesian method of recursive multi-step-ahead density prediction and its ex-post evaluation. We propose a new decomposition of the so-called predictive Bayes factor of order $(k,s)$ into the product of partial Bayes factors. The first factor in the decomposition (called the predictive Bayes factor of order $k$) is related to the relative $k$-period-ahead forecasts ability of models, and the second factor is connected with the recursive updates of posterior odds ratios based on updated data sets. To illustrate the usefulness of the measures proposed, we apply the new decomposed predictive Bayes factors to compare the forecasting ability of models when the true data generating process (DGP) is known. The simulation results suggest that the predictive Bayes factor of order $(k,s)$ introduced here and accounting for the updating effect allows pinpointing the model based on the true DGP. Next, we investigate the predictive ability of different vector error correction models with heteroscedasticity (stochastic volatility and generalized autoregressive conditional heteroskedasticity structures) for sets of the US and Polish macroeconomic variables: unemployment, inflation and interest rates. The results show that the forecasting ability of the models depends on the forecast horizon as well as on taking into account the updating effect.