Testing Equality of Autocovariance Functions

This paper introduces a simple frequency domain test to discern whether two stationary time series have the same autocovariance function. The driving idea is that two stationary short-memory autocovariances coincide over all lags if and only if the corresponding spectral densities agree. As the spectral density is easily estimated via the periodogram, and the asymptotics of the periodogram are well known, a statistic based on the log-ratio of periodogram ordinates is proposed and explored. An application of the method is given. The exposition is made accessible to a general audience, although rudimentary familiarity with spectral densities and periodograms is assumed.