The Annals of Statistics
- Ann. Statist.
- Volume 20, Number 3 (1992), 1426-1440.
Testing Stationarity in the Mean of Autoregressive Processes with a Nonparametric Regression Trend
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.
Ann. Statist., Volume 20, Number 3 (1992), 1426-1440.
First available in Project Euclid: 12 April 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 62G10: Hypothesis testing 62G25
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