Detection of non-constant long memory parameter

Frédéric Lavancier (1) , Remigijus Leipus (2) , Anne Philippe (1) , Donatas Surgailis (2)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 Vilnius Institute of Mathematics and Informatics

This article deals with detection of non-constant long memory parameter in time series. The null hypothesis includes stationary or nonstationary time series with constant long memory parameter, in particular I(d) series, d > −.5. The alternative corresponds to a change in the long memory parameter and gathers in particular an abrupt or gradual change from I(d1) to I(d2), −.5 < d1 < d2. Various test statistics are considered. They are all 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. Moreover, the behavior of the test statistics is studied for some models with 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 considered in some previous works.

Mots clés: Long memory; change in persistence; ratio test; change point; V/S statistic; fractional integration

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Frédéric Lavancier, Remigijus Leipus, Anne Philippe, Donatas Surgailis. Detection of non-constant long memory parameter. 2011. ⟨hal-00634777v1⟩