Bernoulli

Testing temporal constancy of the spectral structure of a time series

Efstathios Paparoditis

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Abstract

Statistical inference for stochastic processes with time-varying spectral characteristics has received considerable attention in recent decades. We develop a nonparametric test for stationarity against the alternative of a smoothly time-varying spectral structure. The test is based on a comparison between the sample spectral density calculated locally on a moving window of data and a global spectral density estimator based on the whole stretch of observations. Asymptotic properties of the nonparametric estimators involved and of the test statistic under the null hypothesis of stationarity are derived. Power properties under the alternative of a time-varying spectral structure are discussed and the behavior of the test for fixed alternatives belonging to the locally stationary processes class is investigated.

Article information

Source
Bernoulli Volume 15, Number 4 (2009), 1190-1221.

Dates
First available in Project Euclid: 8 January 2010

Permanent link to this document
http://projecteuclid.org/euclid.bj/1262962232

Digital Object Identifier
doi:10.3150/08-BEJ179

Mathematical Reviews number (MathSciNet)
MR2597589

Zentralblatt MATH identifier
1200.62049

Citation

Paparoditis, Efstathios. Testing temporal constancy of the spectral structure of a time series. Bernoulli 15 (2009), no. 4, 1190--1221. doi:10.3150/08-BEJ179. http://projecteuclid.org/euclid.bj/1262962232.


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