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Optimal Forecasting of Noncausal Autoregressive Time Series

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  • Lanne, Markku
  • Luoto, Jani
  • Saikkonen, Pentti

Abstract

In this paper, we propose a simulation-based method for computing point and density forecasts for univariate noncausal and non-Gaussian autoregressive processes. Numerical methods are needed to forecast such time series because the prediction problem is generally nonlinear and no analytic solution is therefore available. According to a limited simulation experiment, the use of a correct noncausal model can lead to substantial gains in forecast accuracy over the corresponding causal model. An empirical application to U.S. inflation demonstrates the importance of allowing for noncausality in improving point and density forecasts.

Suggested Citation

  • Lanne, Markku & Luoto, Jani & Saikkonen, Pentti, 2010. "Optimal Forecasting of Noncausal Autoregressive Time Series," MPRA Paper 23648, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:23648
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    References listed on IDEAS

    as
    1. James H. Stock & Mark W. Watson, 2008. "Phillips curve inflation forecasts," Conference Series ; [Proceedings], Federal Reserve Bank of Boston.
    2. Andrews, Beth & Davis, Richard A. & Jay Breidt, F., 2006. "Maximum likelihood estimation for all-pass time series models," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1638-1659, August.
    3. West, Kenneth D, 1996. "Asymptotic Inference about Predictive Ability," Econometrica, Econometric Society, vol. 64(5), pages 1067-1084, September.
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    5. Jonas D. M. Fisher & Chin Te Liu & Ruilin Zhou, 2002. "When can we forecast inflation?," Economic Perspectives, Federal Reserve Bank of Chicago, vol. 26(Q I), pages 32-44.
    6. Lanne, Markku & Luoto, Jani, 2012. "Has US inflation really become harder to forecast?," Economics Letters, Elsevier, vol. 115(3), pages 383-386.
    7. Lanne Markku & Saikkonen Pentti, 2011. "Noncausal Autoregressions for Economic Time Series," Journal of Time Series Econometrics, De Gruyter, vol. 3(3), pages 1-32, October.
    8. Clements, Michael P & Smith, Jeremy, 1999. "A Monte Carlo Study of the Forecasting Performance of Empirical SETAR Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(2), pages 123-141, March-Apr.
    9. Lanne, Markku & Saikkonen, Pentti, 2008. "Modeling Expectations with Noncausal Autoregressions," MPRA Paper 8411, University Library of Munich, Germany.
    10. Valentina Corradi & Norman Swanson, 2006. "Predictive Density Evaluation. Revised," Departmental Working Papers 200621, Rutgers University, Department of Economics.
    11. Lanne, Markku & Nyberg, Henri & Saarinen, Erkka, 2011. "Forecasting U.S. Macroeconomic and Financial Time Series with Noncausal and Causal AR Models: A Comparison," MPRA Paper 30254, University Library of Munich, Germany.
    12. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    13. Jian Huang & Yudi Pawitan, 2000. "Quasi‐likelihood Estimation of Non‐invertible Moving Average Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(4), pages 689-702, December.
    14. Corradi, Valentina & Swanson, Norman R., 2006. "Predictive Density Evaluation," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 5, pages 197-284, Elsevier.
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    Keywords

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    JEL classification:

    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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