Authors: Dette, Holger
Preuß, Philip
Sen, Kemal
Title: Measuring stationarity in long-memory processes
Language (ISO): en
Abstract: In this paper we consider the problem of measuring stationarity in locally stationary longmemory processes. We introduce an L2-distance between the spectral density of the locally stationary process and its best approximation under the assumption of stationarity. The distance is estimated by a numerical approximation of the integrated spectral periodogram and asymptotic normality of the resulting estimate is established. The results can be used to construct a simple test for the hypothesis of stationarity in locally stationary long-range dependent processes. We also propose a bootstrap procedure to improve the approximation of the nominal level and prove its consistency. Throughout the paper, we will work with Riemann sums of a squared periodogram instead of integrals (as it is usually done in the literature) and as a byproduct of independent interest it is demonstrated that the two approaches behave differently in the limit.
Subject Headings: bootstrap
empirical spectral measure
goodness-of-fit tests
integrated periodogram
locally stationary process
non-stationary processes
spectral density
Issue Date: 2013-03-14
Appears in Collections:Sonderforschungsbereich (SFB) 823

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