Parametric Spectral Discrimination

This article is concerned with determining whether two independent time series have been generated by underlying stochastic processes with the same spectral shape. There are many methods that do so using the periodogram. Alternative approaches test for the equality of a finite number of autocovariances or autocorrelations. Non-parametric methods usually have low power when compared with parametric methods. The parametric approach we introduce fits autoregressions to the two time series and tests whether the model parameters are equal using a likelihood ratio test. The test performs well when the time series are from autoregressions. However, problems arise when this is not the case. A modification to the test is proposed, which fits fixed order autoregressions. Simulations show that the modified test performs well even when the two time series are not from autoregressive processes. The parametric approach is shown to outperform non-parametric alternatives in a power study.