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Bootstrap joint prediction regions

  • Michael Wolf
  • Dan Wunderli

Many statistical applications require the forecast of a random variable of interest over several periods into the future. The sequence of individual forecasts, one period at a time, is called a path forecast, where the term path refers to the sequence of individual future realizations of the random variable. The problem of constructing a corresponding joint prediction region has been rather neglected in the literature so far: such a region is supposed to contain the entire future path with a prespecified probability. We develop bootstrap methods to construct joint prediction regions. The resulting regions are proven to be asymptotically consistent under a mild high-level assumption. We compare the finitesample performance of our joint prediction regions to some previous proposals via Monte Carlo simulations. An empirical application to a real data set is also provided.

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Paper provided by Department of Economics - University of Zurich in its series ECON - Working Papers with number 064.

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Date of creation: Feb 2012
Date of revision: May 2013
Handle: RePEc:zur:econwp:064
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  1. De Gooijer, Jan G. & Hyndman, Rob J., 2006. "25 years of time series forecasting," International Journal of Forecasting, Elsevier, vol. 22(3), pages 443-473.
  2. Potter, Simon M, 1995. "A Nonlinear Approach to US GNP," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(2), pages 109-25, April-Jun.
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  6. Joseph P & Romano & Azeem M. Shaikh & Michael Wolf, 2005. "Formalized Data Snooping Based on Generalized Error Rates," IEW - Working Papers 259, Institute for Empirical Research in Economics - University of Zurich.
  7. 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.
  8. James H. Stock & Mark W. Watson, 2001. "Vector Autoregressions," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 101-115, Fall.
  9. Bénédicte Vidaillet & V. D'Estaintot & P. Abécassis, 2005. "Introduction," Post-Print hal-00287137, HAL.
  10. Clements, Michael P. & Taylor, Nick, 2001. "Bootstrapping prediction intervals for autoregressive models," International Journal of Forecasting, Elsevier, vol. 17(2), pages 247-267.
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