STATISTICAL TIME SERIES AND SPATIAL SERIES MODELLING

The present paper is a report on the research works completed during last five years by myself and my Ph. D. students at Peking University in connection with the problems in statistical time series and spatial series modelling. This paper is in two parts. In the first part, we shall give new results of estimating the orders and parameters of the stationary and nonstationary ARMA models (Including stationary ARMA, ARUMA and the general ARMA models). The error terms are supposed to satisfy the martingale difference conditions which are weaker and more natural than supposing them to be i.i.d.. In the second part of this paper, we shall give new results about statistical spatial series modelling. Characterization of twodimensional ARMA models are given. A specific two-dimensional AR model(i. e. the quadrant Markov AR model) is found to be the exact two-dimensional counterpart of the classical onedimensional AR model. For the quadrant Markov AR model, we also give procedures of estimating their orders and parameters.