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April 2015 Detecting gradual changes in locally stationary processes
Michael Vogt, Holger Dette
Ann. Statist. 43(2): 713-740 (April 2015). DOI: 10.1214/14-AOS1297

Abstract

In a wide range of applications, the stochastic properties of the observed time series change over time. The changes often occur gradually rather than abruptly: the properties are (approximately) constant for some time and then slowly start to change. In many cases, it is of interest to locate the time point where the properties start to vary. In contrast to the analysis of abrupt changes, methods for detecting smooth or gradual change points are less developed and often require strong parametric assumptions. In this paper, we develop a fully nonparametric method to estimate a smooth change point in a locally stationary framework. We set up a general procedure which allows us to deal with a wide variety of stochastic properties including the mean, (auto)covariances and higher moments. The theoretical part of the paper establishes the convergence rate of the new estimator. In addition, we examine its finite sample performance by means of a simulation study and illustrate the methodology by two applications to financial return data.

Citation

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Michael Vogt. Holger Dette. "Detecting gradual changes in locally stationary processes." Ann. Statist. 43 (2) 713 - 740, April 2015. https://doi.org/10.1214/14-AOS1297

Information

Published: April 2015
First available in Project Euclid: 3 March 2015

zbMATH: 1312.62045
MathSciNet: MR3319141
Digital Object Identifier: 10.1214/14-AOS1297

Subjects:
Primary: 62G05, 62G20
Secondary: 62M10

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.43 • No. 2 • April 2015
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