Thursday, February 11th, 2010 at 4.10pm, MSB 1147 (Colloquium Room)

Refreshments: 3.30pm, MSB 4110 (Statistics Lounge)

Speaker:       Suhasini Subba Rao (Texas A & M)

Title:                 A test for second order stationarity of a time series based on the Discrete Fourier Transform

Abstract:           We consider a zero mean discrete time series, and define its discrete Fourier transform at the canonical Fourier frequencies. It can be shown that the discrete Fourier transform is asymptotically uncorrelated at the canonical frequencies if and if only the time series is second order stationary. Exploiting this important property, we construct a Portmanteau type test statistic for testing stationarity of the time series. It is shown that under the null of stationarity, the test statistic has approximately a chi square distribution. To examine the power of the test, the asymptotic distribution under the locally stationary alternative is established. It is shown to be a type of noncentral chi-square, where the noncentrality parameter measures the deviation from stationarity. The test is illustrated with simulations, where is it shown to have good power. Some real examples are also included to illustrate the test.