Maximum likelihood estimation of an unknown change-point in the parameters of a multivariate Gaussian series with applications to environmental monitoring

The computable expressions for the asymptotic distribution of the change-point maximum likelihood estimator (mle) were derived when a change occurred in the mean and covariance matrix at an unknown point of a sequence of independently distributed multivariate Gaussian series. The derivation was based on ladder heights of Gaussian random walks hitting the half-line. We then demonstrated that change in a single parameter or change-point analysis in a univariate series can be derived as special cases. A simulation study was carried out to investigate the robustness of the asymptotic distribution to departure from normality, the sample size, location of change-point and amount of change under the multivariate and univariate case. The comparison of the asymptotic mle with Cobb's conditional MLE and Bayesian estimation method using non-informative prior and conjugate prior was also carried out in the simulation study. The asymptotic distribution of the change-point mle was used to compute the confidence interval of the change-point of the stream flows at Northern Quebec Labrador Region and zonal annual mean temperature deviations.