A comparison of multivariate signal discrimination techniques

Abstract

This paper investigates several techniques to discriminate two multivariate stationary signals. The methods considered include Gaussian likelihood ratio tests for variance equality, a chi-squared time-domain test, and a spectral-based test. The latter two tests assess equality of the multivariate autocovariance function of the two signals over many different lags. The Gaussian likelihood ratio test is perhaps best viewed as principal component analyses (PCA) without dimension reduction aspects; it can be modified to consider covariance features other than variances via dimension augmentation tactics. A simulation study is constructed that shows how one can make inappropriate conclusions with PCA tests, even when dimension augmentation techniques are used to incorporate non-zero lag autocovariances into the analysis. The various discrimination methods are first discussed. A simulation study then illuminates the various properties of the methods. In this pursuit, calculations are needed to identify several multivariate time series models with specific autocovariance properties. To demonstrate the applicability of the methods, nine US and Canadian weather stations from three distinct regions are clustered. Here, the spectral clustering perfectly identified distinct regions, the chi-squared test performed marginally, and the PCA/likelihood ratio method did not perform well.