PARAMETER ESTIMATION IN EXPONENTIAL MODELS

Abstract. In this paper the problems of parameter estimation and order determination of an exponential (EX) model are studied in the time domain. In order to estimate the parameters, the parameter equations of an EX model are given in terms of the autocorrelation function, which is similar to the Yule-Walker equations of an autoregressive moving-average model. Estimates of parameters are obtained with the aid of the parameter equations and theorems are proved relating the convergence rate and asymptotic distribution of the estimates. We present two kinds of methods for estimating the order and prove that the estimates of the order are consistent.