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2013 Consistency of minimum description length model selection for piecewise stationary time series models
Richard A. Davis, Chun Yip Yau
Electron. J. Statist. 7: 381-411 (2013). DOI: 10.1214/13-EJS769

Abstract

This paper establishes the consistency of the minimum description length (MDL) model selection procedure by [10, 11] for a class of non-stationary time series models. We consider a time series model in which the observations are viewed as coming from stationary segments. In other words, the data are assumed to come from a general time series model in which the parameters change at break-points. Each of these segments is modeled by a pre-specified family of parametric stationary time series models. [10, 11] formulated the above problem and used the minimum description length (MDL) principle to estimate the number of break-points, the location of the break-points, the order of the parametric model and the parameter values in each of the segments. The procedure performed well on a variety of examples. In this paper we show consistency of their minimal MDL model selection procedure under general regularity conditions on the likelihood function. Results about the rate of convergence of the break-point-location estimator are also given. Applications are considered for detecting changes in independent random variables, and in ARMA and GARCH processes.

Citation

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Richard A. Davis. Chun Yip Yau. "Consistency of minimum description length model selection for piecewise stationary time series models." Electron. J. Statist. 7 381 - 411, 2013. https://doi.org/10.1214/13-EJS769

Information

Published: 2013
First available in Project Euclid: 30 January 2013

zbMATH: 1337.62254
MathSciNet: MR3020426
Digital Object Identifier: 10.1214/13-EJS769

Subjects:
Primary: 62F10, 62M10

Rights: Copyright © 2013 The Institute of Mathematical Statistics and the Bernoulli Society

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