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December 2019 Detecting relevant changes in the mean of nonstationary processes—A mass excess approach
Holger Dette, Weichi Wu
Ann. Statist. 47(6): 3578-3608 (December 2019). DOI: 10.1214/19-AOS1811

Abstract

This paper considers the problem of testing if a sequence of means $(\mu_{t})_{t=1,\ldots ,n}$ of a nonstationary time series $(X_{t})_{t=1,\ldots ,n}$ is stable in the sense that the difference of the means $\mu_{1}$ and $\mu_{t}$ between the initial time $t=1$ and any other time is smaller than a given threshold, that is $|\mu_{1}-\mu_{t}|\leq c$ for all $t=1,\ldots ,n$. A test for hypotheses of this type is developed using a bias corrected monotone rearranged local linear estimator and asymptotic normality of the corresponding test statistic is established. As the asymptotic variance depends on the location of the roots of the equation $|\mu_{1}-\mu_{t}|=c$ a new bootstrap procedure is proposed to obtain critical values and its consistency is established. As a consequence we are able to quantitatively describe relevant deviations of a nonstationary sequence from its initial value. The results are illustrated by means of a simulation study and by analyzing data examples.

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Holger Dette. Weichi Wu. "Detecting relevant changes in the mean of nonstationary processes—A mass excess approach." Ann. Statist. 47 (6) 3578 - 3608, December 2019. https://doi.org/10.1214/19-AOS1811

Information

Received: 1 February 2018; Revised: 1 January 2019; Published: December 2019
First available in Project Euclid: 31 October 2019

Digital Object Identifier: 10.1214/19-AOS1811

Subjects:
Primary: 62F05, 62G08, 62G09, 62M10

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.47 • No. 6 • December 2019
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