MODEL SELECTION AND ORDER DETERMINATION FOR TIME SERIES BY INFORMATION BETWEEN THE PAST AND THE FUTURE

Abstract

Abstract. In this paper, the information between the past and the future of a Gaussian stationary sequence is calculated either by its spectral density or by its autocovariances, and is related to the problem of model fitting. It is demonstrated that the criterion of minimum mutual information is the generalization of that of maximum entropy. By employing the above information quantity, we propose a procedure, which is called LIC for simplicity, to obtain consistent estimate of the order of the Bloomfield model or the autoregressive model. In Monte Carlo studies, we illustrate the LIC procedure by several examples, and also estimate the spectral density of time series by the Bloomfield model and LIC method.