On the Estimation for Compound Poisson Inarch Processes

Abstract

Considering the wide class of discrete Compound Poisson INARCH models, introduced in [6], the main goal of this paper is to develop and compare parametric estimation procedures for first-order models, applicable without specifying the conditional distribution of the process. Therefore, twostep estimation procedures, combining either the conditional least squares (CLS) or the Poisson quasi-maximum likelihood (PQML) methods with that of the moment’s estimation, are introduced and discussed. Specifying the process conditional distribution, we develop also within this class of models the conditional maximum likelihood (CML) methodology. A simulation study illustrates, particularly, the competitive performance of the two-step approaches regarding the more classical CML one which requires the conditional distribution knowledge. A final real-data example shows the relevance of this wide class of models, as it will be clear the better performance in the data fitting of some new models emerging in such class.

Keywords

• integer-valued time series
• CP-INGARCH processes
• estimation