Electronic Journal of Statistics
- Electron. J. Statist.
- Volume 11, Number 1 (2017), 1600-1659.
Detecting long-range dependence in non-stationary time series
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.
Electron. J. Statist., Volume 11, Number 1 (2017), 1600-1659.
Received: July 2016
First available in Project Euclid: 24 April 2017
Permanent link to this document
Digital Object Identifier
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
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