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Combining VAR Forecast Densities Using Fast Fourier Transform

Author

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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.

Suggested Citation

  • Jakub Ryšánek, 2010. "Combining VAR Forecast Densities Using Fast Fourier Transform," Acta Oeconomica Pragensia, University of Economics, Prague, vol. 2010(5), pages 72-88.
    • Handle: RePEc:prg:jnlaop:v:2010:y:2010:i:5:id:318:p:72-88
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    References listed on IDEAS

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    1. Andersson, Michael K & Karlsson, Sune, 2007. "Bayesian forecast combination for VAR models," Working Paper Series 216, Sveriges Riksbank (Central Bank of Sweden).
    2. Marianne Baxter & Robert G. King, 1999. "Measuring Business Cycles: Approximate Band-Pass Filters For Economic Time Series," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 575-593, November.
    3. 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.
    4. 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.
    5. Thomas Doan & Robert B. Litterman & Christopher A. Sims, 1983. "Forecasting and Conditional Projection Using Realistic Prior Distributions," NBER Working Papers 1202, National Bureau of Economic Research, Inc.
    6. Hugo Gerard & Kristoffer Nimark, 2008. "Combining Multivariate Density Forecasts Using Predictive Criteria," RBA Research Discussion Papers rdp2008-02, Reserve Bank of Australia.
    7. Christian Kascha & Francesco Ravazzolo, 2010. "Combining inflation density forecasts," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 29(1-2), pages 231-250.
    8. Wolden Bache, Ida & Sofie Jore, Anne & Mitchell, James & Vahey, Shaun P., 2011. "Combining VAR and DSGE forecast densities," Journal of Economic Dynamics and Control, Elsevier, vol. 35(10), pages 1659-1670, October.
    9. 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.
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    More about this item

    Keywords

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

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • E17 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Forecasting and Simulation: Models and Applications

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