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September, 1992 Testing Stationarity in the Mean of Autoregressive Processes with a Nonparametric Regression Trend
Hartmut Milbrodt
Ann. Statist. 20(3): 1426-1440 (September, 1992). DOI: 10.1214/aos/1176348776

Abstract

In this paper, we suggest tests of stationarity in the mean of autoregressive time series versus arbitrary trend alternatives. As an intermediate, though essential, step local asymptotic normality of autoregressive models with a nonparametric regression trend is established. Moreover, a functional central limit theorem for the underlying likelihood ratio processes is derived. These results then offer a general construction principle by which every goodness of fit test (case 0), which is based on comparing the empirical distribution function and the hypothetical distribution function, corresponds to a test of stationarity in the mean of AR processes. The asymptotic power of these tests is derived. A small simulation study illustrates the performance of Kolmogorov-Smirnov and Cramer-von Mises type tests of stationarity in the mean at hand of a particular AR(2) process.

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Hartmut Milbrodt. "Testing Stationarity in the Mean of Autoregressive Processes with a Nonparametric Regression Trend." Ann. Statist. 20 (3) 1426 - 1440, September, 1992. https://doi.org/10.1214/aos/1176348776

Information

Published: September, 1992
First available in Project Euclid: 12 April 2007

zbMATH: 0781.62140
MathSciNet: MR1186257
Digital Object Identifier: 10.1214/aos/1176348776

Subjects:
Primary: 62M10
Secondary: 62G10, 62G25

Rights: Copyright © 1992 Institute of Mathematical Statistics

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Vol.20 • No. 3 • September, 1992
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