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Model-Based Prediction in Autoregression

  • Dimitris N. Politis
Part of the Frontiers in Probability and the Statistical Sciences book series (FROPROSTAS)

Abstract

In order to construct prediction intervals without the cumbersome—and typically unjustifiable—assumption of Gaussianity, some form of resampling is necessary. The regression set-up has been well-studied in the literature but time series prediction faces additional difficulties. The paper at hand focuses on time series that can be modeled as linear, nonlinear or nonparametric autoregressions, and develops a coherent methodology for the construction of bootstrap prediction intervals. Forward and backward bootstrap methods using predictive and fitted residuals are introduced and compared. We present detailed algorithms for these different models and show that the bootstrap intervals manage to capture both sources of variability, namely the innovation error as well as estimation error. In simulations, we compare the prediction intervals associated with different methods in terms of their achieved coverage level and length of interval.

Notes

Acknowledgements

Chapter  7 is based on the paper: Pan, L. and Politis, D.N. (2015), “Bootstrap prediction intervals for linear, nonlinear and nonparametric autoregressions” (with Discussion), to appear in the Journal of Statistical Planning and Inference. Many thanks are due to the Editors, Anirban DasGupta and Wei-Liem Loh, for hosting this discussion paper, and to the discussants: Silvia Gonçalves, Jae Kim, Jens-Peter Kreiss, Soumen Lahiri, Dan Nordman, and Benoit Perron for their insightful comments.

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© The Author 2015

Authors and Affiliations

  • Dimitris N. Politis
    • 1
  1. 1.Department of MathematicsUniversity of California, San DiegoLa JollaUSA

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