Efficient estimation in semiparametric self-exciting threshold INAR processes

Abstract

This paper focuses on the efficient estimation problem of a more realistic semiparametric SETINAR model of order one with two regimes based on binomial thinning operator. Unlike parametric framework, we do not suppose that the distribution of the innovation process belongs to a parametric family. Instead, the innovation distribution is totally unspecified and is supposed to satisfy only some mild technical assumptions. We, therefore, provide efficient estimators for both parameters of the model, namely a vector of auto-regression parameters and the innovation distribution which is considered as a parameter of infinite-dimension. The performances of these efficient estimators are shown through an intensive simulation study and an application on rotary rig count data in the U.S.A.

KEYWORDS:

• Semiparametric integer-valued process
• Efficient estimation
• LAN property
• Non-parametric maximum likelihood
• SETINAR model

AMS SUBJECT CLASSIFICATION:

• 62F12
• 62M10

Acknowledgments

We are very thankful to the anonymous referees for providing several comments and precious suggestions, and many useful remarks which have enabled us to improve the content and the form of the paper.