Efficient Method of Moments Estimators for Integer Time Series Models ...

Efficient Method of Moments Estimators for Integer Time Series Models Talk to be presented at University Carlos III, Madrid, April 2014 by A.R.Tremayne University of Liverpool Abstract The parameters of integer autoregressive models with equi-dispersed Poisson, or over-dispersed negative binomial innovations can be estimated by maximum likelihood where the prediction error decomposition, together with convolution methods, is used to write down the likelihood function. When a moving average component is introduced this is not the case. In this paper we consider the use of efficient method of moment techniques as a means of obtaining practical estimators of relevant parameters using simulation methods. Under appropriate regularity conditions, the resultant estimators are consistent, asymptotically normal and under certain conditions achieve the same efficiency as maximum likelihood estimators. Simulation evidence on the efficacy of the approach is provided and it is seen that the method can yield serviceable estimates, even with relatively small samples. Estimated standard errors for parameters are obtained using subsampling methods. Applications are in short supply with these models, though the range is increasing. We provide two examples using well-known data sets in the time series literature that have hitherto proved difficult to model satisfactorily; these both require use of specifications with moving average components. Paper co-authored with Vance L. Martin University of Melbourne, Australia and Robert C. Jung Universität Hohenheim, Germany.