TESTS FOR COMPARING TWO ESTIMATED SPECTRAL DENSITIES

Abstract. This paper was motivated by a problem in the gas industry and describes a number of periodogram‐based tests of the hypothesis that two independent time‐series are realizations of the same stationary process. Non‐parametric tests analogous to the maximum periodogram ordinate and cumulative periodogram tests for white noise are compared with a likelihood ratio test based on a postulated quadratic model for the log spectral ratio. The latter is found to be generally more powerful against alternatives in which the two series are realizations of different low order AR processes. The operation of the likelihood ratio test is illustrated by two sets of data, the classic Beveridge wheat price series and a set of data supplied by British Gas.