The Annals of Statistics

Testing Stationarity in the Mean of Autoregressive Processes with a Nonparametric Regression Trend

Hartmut Milbrodt

Full-text: Open access

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.

Article information

Source
Ann. Statist., Volume 20, Number 3 (1992), 1426-1440.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176348776

Digital Object Identifier
doi:10.1214/aos/1176348776

Mathematical Reviews number (MathSciNet)
MR1186257

Zentralblatt MATH identifier
0781.62140

JSTOR
links.jstor.org

Subjects
Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 62G10: Hypothesis testing 62G25

Keywords
Autoregressive processes nonparametric regression local asymptotic normality (LAN) LAW structure tests of stationarity in the mean

Citation

Milbrodt, Hartmut. Testing Stationarity in the Mean of Autoregressive Processes with a Nonparametric Regression Trend. Ann. Statist. 20 (1992), no. 3, 1426--1440. doi:10.1214/aos/1176348776. https://projecteuclid.org/euclid.aos/1176348776


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