Spectral decomposition of the AR metric

This work investigates a spectral decomposition of the AR metric proposed as a measure of structural dissimilarity among ARIMA processes. Specifically, the metric will be related to the variance of a stationary process so that its behaviour in the frequency domain will help to detect how unobserved components generated by the parameters of both phenomena concur in specifying the obtained distance. Foundations for the metric are briefly reminded and the main consequences of the proposed decomposition are discussed with special reference to some specific stochastic processes in order to improve the interpretative content of the AR metric.