Testing temporal constancy of the spectral structure of a time series

Details Testing temporal constancy of the spectral structure of a time series Testing temporal constancy of the spectral structure of a time series

2010-01-13

arxiv.org/abs/1001.2122v1

Bernoulli 2009, Vol. 15, No. 4, 1190-1221

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.3150/08-BEJ179 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/08-BEJ179

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.

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