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Comparing several methods to compute joint prediction regions for path forecasts generated by vector autoregressions

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  • Stefan Bruder

Abstract

Path forecasts, defined as sequences of individual forecasts, generated by vector autoregressions are widely used in applied work. It has been recognized that a profound econometric analysis often requires, besides the path forecast, a joint prediction region that contains the whole future path with a prespecified coverage probability. The forecasting literature offers several different methods for computing joint prediction regions, where the existing methods are either bootstrap based or rely on asymptotic results. The aim of this paper is to investigate the finite-sample performance of three methods for constructing joint prediction regions in various scenarios via Monte Carlo simulations.

Suggested Citation

  • Stefan Bruder, 2014. "Comparing several methods to compute joint prediction regions for path forecasts generated by vector autoregressions," ECON - Working Papers 181, Department of Economics - University of Zurich, revised Dec 2015.
    • Handle: RePEc:zur:econwp:181
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    File URL: https://www.zora.uzh.ch/id/eprint/101244/7/econwp181.pdf
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    References listed on IDEAS

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    1. Amihud, Yakov & Hurvich, Clifford M., 2004. "Predictive Regressions: A Reduced-Bias Estimation Method," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 39(4), pages 813-841, December.
    2. Kim, Jae H, 2001. "Bootstrap-after-Bootstrap Prediction Intervals for Autoregressive Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(1), pages 117-128, January.
    3. John Galbraith & Aman Ullah & Victoria Zinde-Walsh, 2002. "Estimation Of The Vector Moving Average Model By Vector Autoregression," Econometric Reviews, Taylor & Francis Journals, vol. 21(2), pages 205-219.
    4. Michael D. Bauer & Glenn D. Rudebusch & Jing Cynthia Wu, 2012. "Correcting Estimation Bias in Dynamic Term Structure Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(3), pages 454-467, April.
    5. Tom Engsted & Thomas Q. Pedersen, 2014. "Bias-Correction in Vector Autoregressive Models: A Simulation Study," Econometrics, MDPI, vol. 2(1), pages 1-27, March.
    6. Òscar Jordà & Massimiliano Marcellino, 2010. "Path forecast evaluation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(4), pages 635-662.
    7. Taku Yamamoto & Naoto Kunitomo, 1981. "Asymptotic Bias of Ordinary Least Squares Estimator for Multivariate Autoregressive Models," Discussion Papers 504, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    8. Yakov Amihud & Clifford M. Hurvich & Yi Wang, 2009. "Multiple-Predictor Regressions: Hypothesis Testing," The Review of Financial Studies, Society for Financial Studies, vol. 22(1), pages 413-434, January.
    9. Bénédicte Vidaillet & V. d'Estaintot & P. Abécassis, 2005. "Introduction," Post-Print hal-00287137, HAL.
    10. Frank Schorfheide & Dongho Song, 2015. "Real-Time Forecasting With a Mixed-Frequency VAR," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(3), pages 366-380, July.
    11. James H. Stock & Mark W. Watson, 2001. "Vector Autoregressions," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 101-115, Fall.
    12. Clifford M. Hurvich & Chih‐Ling Tsai, 1993. "A Corrected Akaike Information Criterion For Vector Autoregressive Model Selection," Journal of Time Series Analysis, Wiley Blackwell, vol. 14(3), pages 271-279, May.
    13. Michael Wolf & Dan Wunderli, 2012. "Bootstrap joint prediction regions," ECON - Working Papers 064, Department of Economics - University of Zurich, revised May 2013.
    14. Kilian, Lutz, 2001. "Impulse Response Analysis in Vector Autoregressions with Unknown Lag Order," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 20(3), pages 161-179, April.
    15. Pascual, Lorenzo & Fresoli, Diego Eduardo, 2011. "Bootstrap forecast of multivariate VAR models without using the backward representation," DES - Working Papers. Statistics and Econometrics. WS ws113426, Universidad Carlos III de Madrid. Departamento de Estadística.
    16. Staszewska-Bystrova, Anna & Winker, Peter, 2013. "Constructing narrowest pathwise bootstrap prediction bands using threshold accepting," International Journal of Forecasting, Elsevier, vol. 29(2), pages 221-233.
    17. Brent Meyer & Saeed Zaman, 2013. "It’s not just for inflation: The usefulness of the median CPI in BVAR forecasting," Working Papers (Old Series) 1303, Federal Reserve Bank of Cleveland.
    18. Anna Staszewska‐Bystrova, 2011. "Bootstrap prediction bands for forecast paths from vector autoregressive models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 30(8), pages 721-735, December.
    19. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
    20. Staszewska-Bystrova Anna, 2013. "Modified Scheffé’s Prediction Bands," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 233(5-6), pages 680-690, October.
    21. Lutz Kilian, 1998. "Small-Sample Confidence Intervals For Impulse Response Functions," The Review of Economics and Statistics, MIT Press, vol. 80(2), pages 218-230, May.
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    More about this item

    Keywords

    Path forecast; joint prediction region; Monte Carlo simulation;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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