Rényi statistics for testing equality of autocorrelation coefficients

The problem of testing for equality of autocorrelation coefficients of two populations in multivariate data when errors are autocorrelated is considered. We derive Rényi statistics defined as divergences between unrestricted and restricted estimated joint probability density functions and we show that they are asymptotically chi-square distributed under the null hypothesis of interest. Monte Carlo simulation experiments are carried out to investigate the behavior of Rényi statistics and to make comparisons with test statistics based on the approach of Bhandary M. Bhandary, Test for equality of autocorrelation coefficients for two populations in multivariate data when the errors are autocorrelated, Statistics & Probability Letters 73 (2005) 333–342] for the problem under consideration. Rényi statistics showed to have significantly better behavior.