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Bootstrap joint prediction regions


Wolf, Michael; Wunderli, Dan (2015). Bootstrap joint prediction regions. Journal of Time Series Analysis, 36(3):352-376.

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 finite-sample performance of our joint prediction regions with some previous proposals via Monte Carlo simulations. An empirical application to a real data set is also provided.

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 finite-sample performance of our joint prediction regions with some previous proposals via Monte Carlo simulations. An empirical application to a real data set is also provided.

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3 citations in Web of Science®
3 citations in Scopus®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Economics
Dewey Decimal Classification:330 Economics
Uncontrolled Keywords:Generalized error rates, path forecast, simultaneous prediction intervals
Language:English
Date:2015
Deposited On:14 Oct 2015 13:31
Last Modified:05 Apr 2016 19:26
Publisher:Wiley-Blackwell Publishing, Inc.
ISSN:0143-9782
Additional Information:Special Issue: Recent developments in bootstrap methods for dependent data / This is the peer reviewed version of the following article: [Wolf, M., and Wunderli, D. (2015), Bootstrap Joint Prediction Regions. J. Time Ser. Anal., 36, 352–376. doi: 10.1111/jtsa.12099], which has been published in final form at [http://doi.org/10.1111/jtsa.12099]. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.
Publisher DOI:https://doi.org/10.1111/jtsa.12099
Permanent URL: https://doi.org/10.5167/uzh-113354

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