Lei Jin
Mathematics, Computer Science and Statistics Department
McNeese State University
Friday, February 22, 2013

Richardson Hall 224

A new nonparametric stationarity test of time series in time domain

Abstract: 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 are defined via the Walsh functions. The test is to detect whether there is any non-constant covariance structure over time, by checking the deviations from the autocovariances on systematic samples to the corresponding autocovariances of the whole time series. The asymptotic distribution of these deviations is obtained.  Interestingly, these deviations of different systematic samples are asymptotically independent. A double order selection scheme is used to combine the deviations at different lags in the systematic samples. The null asymptotic distribution of the proposed statistic is derived and the consistency of the test under some general/local alternatives is shown. A simulation study demonstrates well-behaved finite sample properties of the proposed method. In addition, the proposed method is applied to check the stationarity assumption of a chemical process viscosity readings data.