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Detection of nonconstant long memory parameter. (English) Zbl 1290.62062
Summary: This article deals with detection of a nonconstant long memory parameter in time series. The null hypothesis presumes stationary or nonstationary time series with a constant long memory parameter, typically an I(\(d\)) series with \(d>-.5\). The alternative corresponds to an increase in persistence and includes in particular an abrupt or gradual change from I(\(d_{1}\)) to I(\(d_{2}\)), \(-.5<d_{1}<d_{2}\). We discuss several test statistics based on the ratio of forward and backward sample variances of the partial sums. The consistency of the tests is proved under a very general setting. We also study the behavior of these test statistics for some models with a changing memory parameter. A simulation study shows that our testing procedures have good finite sample properties and turn out to be more powerful than the KPSS-based tests [D. Kwiatkowski et al., J. Econom. 54, No. 1–3, 159–178 (1992; Zbl 0871.62100)] considered in some previous works.

MSC:
62M07 Non-Markovian processes: hypothesis testing
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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