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Bootstrap prediction bands for forecast paths from vector autoregressive models

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  • Anna Staszewska‐Bystrova

Abstract

The problem of forecasting from vector autoregressive models has attracted considerable attention in the literature. The most popular non-Bayesian approaches use either asymptotic approximations or bootstrapping to evaluate the uncertainty associated with the forecast. The practice in the empirical literature has been to assess the uncertainty of multi‐step forecasts by connecting the intervals constructed for individual forecast periods. This paper proposes a bootstrap method of constructing prediction bands for forecast paths. The bands are constructed from forecast paths obtained in bootstrap replications using an optimization procedure to find the envelope of the most concentrated paths. From extensive Monte Carlo study, it is found that the proposed method provides more accurate assessment of predictive uncertainty from the vector autoregressive model than its competitors. Copyright (C) 2010 John Wiley & Sons, Ltd.

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File URL: http://hdl.handle.net/10.1002/for.1205
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Bibliographic Info

Article provided by John Wiley & Sons, Ltd. in its journal Journal of Forecasting.

Volume (Year): 30 (2011)
Issue (Month): 8 (December)
Pages: 721-735

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Handle: RePEc:jof:jforec:v:30:y:2011:i:8:p:721-735

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Web page: http://www3.interscience.wiley.com/cgi-bin/jhome/2966

Related research

Keywords: vector autoregression ; forecast path ; bootstrap ; simultaneous statistical inference ;

References

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  1. Anna Staszewska, 2006. "Representing Uncertainty about Response Paths: the Use of Heuristic Optimisation Methods," Computing in Economics and Finance 2006 379, Society for Computational Economics.
  2. Clements, Michael P. & Kim, Jae H., 2007. "Bootstrap prediction intervals for autoregressive time series," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3580-3594, April.
  3. Kim, Jae H, 2002. "Bootstrap Prediction Intervals for Autoregressive Models of Unknown or Infinite Lag Order," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 21(4), pages 265-80, July.
  4. Masarotto, Guido, 1990. "Bootstrap prediction intervals for autoregressions," International Journal of Forecasting, Elsevier, vol. 6(2), pages 229-239, July.
  5. 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.
  6. Jae H. Kim, 2004. "Bias-corrected bootstrap prediction regions for vector autoregression," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 23(2), pages 141-154.
  7. Clements, Michael P. & Taylor, Nick, 2001. "Bootstrapping prediction intervals for autoregressive models," International Journal of Forecasting, Elsevier, vol. 17(2), pages 247-267.
  8. Kim, Jae H, 2001. "Bootstrap-after-Bootstrap Prediction Intervals for Autoregressive Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(1), pages 117-28, January.
  9. James H. Stock & Mark W. Watson, 2001. "Vector Autoregressions," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 101-115, Fall.
  10. Kim, Jae H., 1999. "Asymptotic and bootstrap prediction regions for vector autoregression," International Journal of Forecasting, Elsevier, vol. 15(4), pages 393-403, October.
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Citations

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Cited by:
  1. Lorenzo Pascual & Esther Ruiz & Diego Fresoli, 2011. "Bootstrap forecast of multivariate VAR models without using the backward representation," Statistics and Econometrics Working Papers ws113426, Universidad Carlos III, Departamento de Estadística y Econometría.
  2. Anna Staszewska-Bystrova, 2013. "Modified Scheffé’s Prediction Bands," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), Justus-Liebig University Giessen, Department of Statistics and Economics, vol. 233(5-6), pages 680-690, October.
  3. Bystrov, Victor, 2013. "A factor-augemented model of markup on mortgage loans in Poland," MPRA Paper 49683, University Library of Munich, Germany.
  4. Helmut Lütkepohl & Anna Staszewska-Bystrova & Peter Winker, 2013. "Comparison of Methods for Constructing Joint Confidence Bands for Impulse Response Functions," SFB 649 Discussion Papers SFB649DP2013-031, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  5. Michael Wolf & Dan Wunderli, 2012. "Bootstrap joint prediction regions," ECON - Working Papers 064, Department of Economics - University of Zurich, revised May 2013.
  6. Jordà, Òscar & Knüppel, Malte & Marcellino, Massimiliano, 2013. "Empirical simultaneous prediction regions for path-forecasts," International Journal of Forecasting, Elsevier, vol. 29(3), pages 456-468.
  7. Helmut Lütkepohl & Anna Staszewska-Bystrova & Peter Winker, 2014. "Confidence Bands for Impulse Responses: Bonferroni versus Wald," Discussion Papers of DIW Berlin 1354, DIW Berlin, German Institute for Economic Research.
  8. 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.

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