Bernoulli

Piecewise quantile autoregressive modeling for nonstationary time series

Alexander Aue, Rex C.Y. Cheung, Thomas C.M. Lee, and Ming Zhong

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Abstract

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.

Article information

Source
Bernoulli, Volume 23, Number 1 (2017), 1-22.

Dates
Received: January 2014
Revised: July 2014
First available in Project Euclid: 27 September 2016

Permanent link to this document
https://projecteuclid.org/euclid.bj/1475001346

Digital Object Identifier
doi:10.3150/14-BEJ671

Mathematical Reviews number (MathSciNet)
MR3556764

Zentralblatt MATH identifier
1378.62056

Keywords
autoregressive time series change-point genetic algorithm minimum description length principle nonstationary time series structural break

Citation

Aue, Alexander; Cheung, Rex C.Y.; Lee, Thomas C.M.; Zhong, Ming. Piecewise quantile autoregressive modeling for nonstationary time series. Bernoulli 23 (2017), no. 1, 1--22. doi:10.3150/14-BEJ671. https://projecteuclid.org/euclid.bj/1475001346


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