Estimation on a GAR(1) Process by the EM Algorithm

Abstract Because of the increasing number of interrelated processes continuous monitoring and controlling of processes get more and more important. Time series constitute one possibility of modelling processes in order to determine an appropriate monitoring policy. One major problem when deriving a time series consists of estimating the values of the relevant parameters. This paper deals with the estimation of the parameters of a first order autoregressive gamma process by means of the EM algorithm. The formulae of the EM sequence are derived, the convergence of the procedure is established and the results of a simulation study are presented. The EM algorithm proves to be an appropriate estimation procedure in the case of the complex statistical model represented by a GAR(1) process.