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2017 Detecting long-range dependence in non-stationary time series
Holger Dette, Philip Preuss, Kemal Sen
Electron. J. Statist. 11(1): 1600-1659 (2017). DOI: 10.1214/17-EJS1262


An important problem in time series analysis is the discrimination between non-stationarity and long-range dependence. Most of the literature considers the problem of testing specific parametric hypotheses of non-stationarity (such as a change in the mean) against long-range dependent stationary alternatives. In this paper we suggest a simple approach, which can be used to test the null-hypothesis of a general non-stationary short-memory against the alternative of a non-stationary long-memory process. The test procedure works in the spectral domain and uses a sequence of approximating tvFARIMA models to estimate the time varying long-range dependence parameter. We prove uniform consistency of this estimate and asymptotic normality of an averaged version. These results yield a simple test (based on the quantiles of the standard normal distribution), and it is demonstrated in a simulation study that - despite of its semi-parametric nature - the new test outperforms the currently available methods, which are constructed to discriminate between specific parametric hypotheses of non-stationarity short- and stationarity long-range dependence.


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Holger Dette. Philip Preuss. Kemal Sen. "Detecting long-range dependence in non-stationary time series." Electron. J. Statist. 11 (1) 1600 - 1659, 2017.


Received: 1 July 2016; Published: 2017
First available in Project Euclid: 24 April 2017

zbMATH: 1362.62164
MathSciNet: MR3638972
Digital Object Identifier: 10.1214/17-EJS1262

Primary: 62M10 , 62M15
Secondary: 62G10

Keywords: approximating models , empirical spectral measure , Goodness-of-fit tests , integrated periodogram , locally stationary process , long-memory , non-stationary processes , Spectral density


Vol.11 • No. 1 • 2017
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