Electronic Journal of Statistics

Detecting long-range dependence in non-stationary time series

Holger Dette, Philip Preuss, and Kemal Sen

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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.

Article information

Electron. J. Statist., Volume 11, Number 1 (2017), 1600-1659.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84] 62M15: Spectral analysis
Secondary: 62G10: Hypothesis testing

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

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Dette, Holger; Preuss, Philip; Sen, Kemal. Detecting long-range dependence in non-stationary time series. Electron. J. Statist. 11 (2017), no. 1, 1600--1659. doi:10.1214/17-EJS1262. https://projecteuclid.org/euclid.ejs/1493020822

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