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June, 1995 Testing a Time Series for Difference Stationarity
B. P. M. McCabe, A. R. Tremayne
Ann. Statist. 23(3): 1015-1028 (June, 1995). DOI: 10.1214/aos/1176324634


This paper addresses the problem of testing the hypothesis that an observed series is difference stationary. The alternative hypothesis is that the series is another nonstationary process; in particular, an autoregressive model with a random parameter is used. A locally best invariant test is developed assuming Gaussianity, and a representation of its asymptotic distribution as a mixture of Brownian motions is found. The performance of the test in finite samples is investigated by simulation. An example is given where the difference stationary assumption for a well-known data series is rejected.


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B. P. M. McCabe. A. R. Tremayne. "Testing a Time Series for Difference Stationarity." Ann. Statist. 23 (3) 1015 - 1028, June, 1995.


Published: June, 1995
First available in Project Euclid: 11 April 2007

zbMATH: 0838.62082
MathSciNet: MR1345212
Digital Object Identifier: 10.1214/aos/1176324634

Primary: 62M10
Secondary: 62F03 , 62F05

Keywords: Autoregression , Brownian motion , difference stationarity , Locally best invariant , random coefficient , weak convergence

Rights: Copyright © 1995 Institute of Mathematical Statistics


Vol.23 • No. 3 • June, 1995
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