On testing for homogeneity of several autoregressive processes

Abstract

An informal Bayesian analysis is taken to test the hypothesis that several autoregressive processes are the same. The common order of the processes is known, but the other parameters are unknown. Assuming white noise for the inputs and a vague prior density for the parameters, the test for homogeneity is based on the region of highest posterior density of the autoregressive coefficients. The test is equivalent to an F-test. The methodology is illustrated with two first-order processes, and a numerical example using generated data demonstrates that the Bayes approach is reasonable.