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Bootstrap joint prediction regions

Author

Listed:
  • Michael Wolf
  • Dan Wunderli

Abstract

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.

Suggested Citation

  • Michael Wolf & Dan Wunderli, 2012. "Bootstrap joint prediction regions," ECON - Working Papers 064, Department of Economics - University of Zurich, revised May 2013.
    • Handle: RePEc:zur:econwp:064
    as

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    File URL: https://www.zora.uzh.ch/id/eprint/60385/6/econwp064.pdf
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Generalized error rates; path forecast; simultaneous prediction intervals;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric 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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