Parameter estimation for INAR processes based on high-order statistics

Abstract

The high-order statistics (moments and cumulants of order higher than two) have been widely applied in several fields, specially in problems where it is conjectured a lack of Gaussianity and/or non-linearity. Since the INteger-valued AutoRegressive, INAR, processes are non-Gaussian, the high-order statistics can provide additional information that allows a better characterization of these processes. Thus, an estimation method for the parameters of an INAR process, based on Least Squares for the third-order moments is proposed. The results of a Monte Carlo study to investigate the performance of the estimator are presented and the method is applied to a set of real data.