Testing for long memory in the presence of a general trend. (English) Zbl 1140.62341

Giraitis, Liudas; Kokoszka, Piotr; Leipus, Remigijus

J. Appl. Probab. 38, No. 4, 1033-1054 (2001).

Summary: The paper studies the impact of a broadly understood trend, which includes a change point in mean and monotonic trends studied by Bhattacharya et al. (1983), on the asymptotic behaviour of a class of tests designed to detect long memory in a stationary sequence. Our results pertain to a family of tests which are similar to Lo’s (1991) modified \(R/S\) test. We show that both long memory and nonstationarity (presence of trend or change points) can lead to rejection of the null hypothesis of short memory, so that further testing is needed to discriminate between long memory and some forms of nonstationarity. We provide quantitative description of trends which do or do not fool the \(R/S\)-type long memory tests. We show, in particular, that a shift in mean of a magnitude larger than \(N^{-1/2}\), where \(N\) is the sample size, affects the asymptotic size of the tests, whereas smaller shifts do not do so.

MSC:

62M10	Time series, auto-correlation, regression, etc. in statistics (GARCH)
62M05	Markov processes: estimation; hidden Markov models

Keywords:

change point