Combining VAR Forecast Densities Using Fast Fourier Transform

In this paper, I propose the use of fast Fourier transform (FFT) as a convenient tool for combining forecast densities of vector autoregressive models in a hybrid Bayesian manner. While a vast amount of papers comprises combinations based on normal approximations, Monte Carlo methods were fully utilized here, which made the analysis computationally demanding. For the sake of minimization of computational time, the FFT algorithm was used to combine the densities of poorly simulated partial models. As a result, a minor loss of quality in the final combined model was allowed, in contrast with the reduction in the necessary simulation time. However, it turns out in the end that the FFT-based approach exceeds ´brute-force´ simulation in all aspects. The suggested method is demonstrated on an ex ante prediction of the Czech GDP and on a pair of artificial examples.