Abstract
© 2015 The Royal Statistical Society and Blackwell Publishing Ltd. We propose a new double-order selection test for checking second-order stationarity of a time series. To develop the test, a sequence of systematic samples is defined via Walsh functions. Then the deviations of the autocovariances based on these systematic samples from the corresponding autocovariances of the whole time series are calculated and the uniform asymptotic joint normality of these deviations over different systematic samples is obtained. With a double-order selection scheme, our test statistic is constructed by combining the deviations at different lags in the systematic samples. The null asymptotic distribution of the statistic proposed is derived and the consistency of the test is shown under fixed and local alternatives. Simulation studies demonstrate well-behaved finite sample properties of the method proposed. Comparisons with some existing tests in terms of power are given both analytically and empirically. In addition, the method proposed is applied to check the stationarity assumption of a chemical process viscosity readings data set.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 893-922 |
| Number of pages | 30 |
| Journal | Journal of the Royal Statistical Society: Series B (Statistical Methodology) |
| Volume | 77 |
| Issue number | 5 |
| DOIs | |
| State | Published - Nov 7 2014 |
| Externally published | Yes |
Bibliographical note
KAUST Repository Item: Exported on 2020-10-01Acknowledged KAUST grant number(s): KUS-CI-016-04
Acknowledgements: We thank two Joint Editors, an Associate Editor and two referees for their helpful comments and suggestions that have led to a much improved version of this paper. S. Wang's research was partially supported by award KUS-CI-016-04, made by King Abdullah University of Science and Technology. H. Wang's research was partially supported by a grant from the Simons Foundation (246077). Part of the work was carried out while S. Wang was visiting the Australian National University supported by the Mathematical Sciences Research Visitor Programme.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.