Open Access
February 2017 Piecewise quantile autoregressive modeling for nonstationary time series
Alexander Aue, Rex C.Y. Cheung, Thomas C.M. Lee, Ming Zhong
Bernoulli 23(1): 1-22 (February 2017). DOI: 10.3150/14-BEJ671


We develop a new methodology for the fitting of nonstationary time series that exhibit nonlinearity, asymmetry, local persistence and changes in location scale and shape of the underlying distribution. In order to achieve this goal, we perform model selection in the class of piecewise stationary quantile autoregressive processes. The best model is defined in terms of minimizing a minimum description length criterion derived from an asymmetric Laplace likelihood. Its practical minimization is done with the use of genetic algorithms. If the data generating process follows indeed a piecewise quantile autoregression structure, we show that our method is consistent for estimating the break points and the autoregressive parameters. Empirical work suggests that the proposed method performs well in finite samples.


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Alexander Aue. Rex C.Y. Cheung. Thomas C.M. Lee. Ming Zhong. "Piecewise quantile autoregressive modeling for nonstationary time series." Bernoulli 23 (1) 1 - 22, February 2017.


Received: 1 January 2014; Revised: 1 July 2014; Published: February 2017
First available in Project Euclid: 27 September 2016

zbMATH: 1378.62056
MathSciNet: MR3556764
Digital Object Identifier: 10.3150/14-BEJ671

Keywords: autoregressive time series , Change-point , Genetic algorithm , minimum description length principle , nonstationary time series , structural break

Rights: Copyright © 2017 Bernoulli Society for Mathematical Statistics and Probability

Vol.23 • No. 1 • February 2017
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