Does the dispersion matrix of a multivariate normal population have markov structures?

Abstract

Given the sequence of variables x₀,x₁,…,x_m we show how to test the hypothesis that, for each j and t < j, the conditional distribution of x_j given (x₀,x₁,…,x_t) is free of (x₀,x₁,…,x_t−1). Our assumptions are that the population from which the sequence is drawn has a multivariate normal density and that the population may be sampled repeatedly.

Keywords:

• Markov structure
• test dispersion matrix
• multivariate normal and multivariate & densities