Junho Yang, Academia Sinica
Project Description/Abstract
Test for stationarity of time series data is considered an important procedure to validate the estimation and prediction results. [Dwivedi and Subba Rao (2011)] developed a test in the frequency domain, where the test statistic is constructed based on the Discrete Fourier transform (DFT) of an observed time series. However, due to the finite sample bias, the test statistic may have an inflated false positive rate for small sample time series. In this paper, we develop a new frequency domain test statistic that is completely unbiased under the null of stationarity. The derivation hinges on obtaining a linear transform of an observed time series which is biorthogonal to the DFT of a stationary time series. This linear transform is a function of infinite order autoregressive coefficients of stationary time series and in general, it has no closed-form solution. We obtain an approximation for the test statistic by fitting a finite order autoregressive process. We show that the approximated test statistic yields a smaller bias under the null. We derive an asymptotic distribution of test statistic under both null and alternative of local stationarity and we show that the test has power approaching to one. The proposed method is illustrated with simulations.
Co-author
Alex Coulter, Texas A&M University