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Combining VAR Forecast Densities Using Fast Fourier Transform

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  • Jakub Ryšánek

Abstract

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.

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Bibliographic Info

Article provided by University of Economics, Prague in its journal Acta Oeconomica Pragensia.

Volume (Year): 2010 (2010)
Issue (Month): 5 ()
Pages: 72-88

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Handle: RePEc:prg:jnlaop:v:2010:y:2010:i:5:id:318:p:72-88

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Related research

Keywords: vector autoregressions; Markov chain Monte Carlo; fast Fourier transform; Bayesian model averaging;

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References

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  1. Ida Wolden Bache & Anne Sofie Jore & James Mitchell & Shaun P. Vahey, 2009. "Combining VAR and DSGE forecast densities," Working Paper 2009/23, Norges Bank.
  2. Marianne Baxter & Robert G. King, 1995. "Measuring Business Cycles Approximate Band-Pass Filters for Economic Time Series," NBER Working Papers 5022, National Bureau of Economic Research, Inc.
  3. Christian Kascha & Francesco Ravazzolo, 2008. "Combining inflation density forecasts," Working Paper 2008/22, Norges Bank.
  4. Litterman, Robert B, 1986. "Forecasting with Bayesian Vector Autoregressions-Five Years of Experience," Journal of Business & Economic Statistics, American Statistical Association, vol. 4(1), pages 25-38, January.
  5. Xavier Sala-I-Martin & Gernot Doppelhofer & Ronald I. Miller, 2004. "Determinants of Long-Term Growth: A Bayesian Averaging of Classical Estimates (BACE) Approach," American Economic Review, American Economic Association, vol. 94(4), pages 813-835, September.
  6. Andersson, Michael K & Karlsson, Sune, 2007. "Bayesian forecast combination for VAR models," Working Paper Series 216, Sveriges Riksbank (Central Bank of Sweden).
  7. Mark W. Watson & James H. Stock, 2004. "Combination forecasts of output growth in a seven-country data set," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 23(6), pages 405-430.
  8. Hugo Gerard & Kristoffer Nimark, 2008. "Combining multivariate density forecasts using predictive criteria," Economics Working Papers 1117, Department of Economics and Business, Universitat Pompeu Fabra, revised Oct 2008.
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