A test for second-order stationarity of time series based on unsystematic subsamples

Haeran Cho (University of Bristol)

Friday 11th March, 2016 15:00-16:00 Maths 522

Abstract

In this talk, we introduce a new method for testing the stationarity
of time series, where the test statistic is obtained from measuring
and maximising the difference in the second-order structure over pairs
of randomly drawn intervals. The asymptotic normality of the test
statistic is established for both Gaussian and a range of non-Gaussian
time series, and a bootstrap procedure is proposed for estimating the
variance of the main statistics. Further, we show the consistency of
our test under fixed and local alternatives. Due to the flexibility
inherent in the random, unsystematic subsamples used for test
statistic construction, the proposed method is able to identify the
intervals of significant departure from the stationarity without any
dyadic constraints, which is an advantage over other tests employing
systematic designs. We demonstrate its good finite sample performance
on both simulated and real data, particularly in detecting localised
departure from the stationarity.

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