Testing Equality of Stationary Autocovariances

Abstract

This paper studies tests for assessing whether two stationary and independent time series have the same dynamics, specifically, whether the autocovariances of both series coincide at all lags. Several frequency domain statistics previously proposed for this purpose are reviewed. A time domain statistic is then developed and investigated. The performance of these statistics are compared. As the previous literature on this topic resides almost exclusively within the spectral domain, it is perhaps surprising that the time domain test outperforms the frequency domain tests. Multivariate versions of the results are then investigated. The methods are applied in the analysis of temperatures and precipitations from two towns in the state of Georgia. Our interest here is driven by the need to identify a good climatological reference series for a given station. Efforts are made to keep the exposition rudimentary and expository.