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 long-memory non-stationary processes spectral density |
URI: | http://hdl.handle.net/2003/30097 http://dx.doi.org/10.17877/DE290R-10344 |
Issue Date: | 2013-03-14 |
Appears in Collections: | Sonderforschungsbereich (SFB) 823 |
Files in This Item:
File | Description | Size | Format | |
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DP_0913_SFB823_Sen_Preuß_Dette.pdf | DNB | 515.08 kB | Adobe PDF | View/Open |
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