Combining Var Forecast Densities Using Fast Fourier Transform

In this paper, I propose the use of fast Fourier transform (FFT) as a convenienttool for combining forecast densities of vector autoregressive models in a hybrid Bayesianmanner. While a vast amount of papers comprises combinations based on normal approxi-mations, Monte Carlo methods were fully utilized here, which made the analysis computa-tionally demanding. For the sake of minimization of computational time, the FFT algorithmwas used to combine the densities of poorly simulated partial models. As a result, a minorloss of quality in the fi nal combined model was allowed, in contrast with the reduction in thenecessary simulation time. However, it turns out in the end that the FFT-based approachexceeds ‘brute-force’ simulation in all aspects. The suggested method is demonstrated onan ex ante prediction of the Czech GDP and on a pair of artifi cial examples.