Penalized estimation for integer autoregressive models

Abstract

The integer autoregressive model of order p can be employed for the analysis of discrete-valued time series data. It can be shown, under some conditions, that its correlation structure is identical to that of the usual autoregressive process. The model is usually fitted by the method of least squares. However, consider an alternative estimation scheme, which is based on minimizing the least squares criterion subject to some constraints on the parameters of interest. The ridge type of constraints are used in this article and it is shown that under some reasonable conditions on the penalty parameter, the resulting estimates have lessmean square error than that of the ordinary least squares. A real data set and some limited simulations support further the results. © 2010 Springer-Verlag Berlin Heidelberg.