Testing equality of stationary autocovariances

This article 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. 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. Multivariate versions of the results are constructed. The methods are applied in the analysis of temperatures and precipitations from Atlanta and Athens, Georgia. Our interest here is driven by the need to identify a good climatological reference series for a given station.