Piecewise quantile autoregressive modeling for nonstationary time series

TL;DR

This paper introduces a novel piecewise quantile autoregressive modeling approach for nonstationary time series, effectively capturing complex distributional changes and nonlinearity, with proven consistency and good finite-sample performance.

Contribution

It proposes a new methodology for modeling nonstationary time series using piecewise stationary quantile autoregressive processes with model selection via minimum description length.

Findings

Method is consistent for estimating break points and parameters.

Performs well in finite samples.

Effective for complex nonstationary data.

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.