Consistency of a nonparametric least squares estimator in integer-valued GARCH models

Abstract

We consider a nonparametric version of the integer-valued GARCH(1,1) model for time series of counts. The link function in the recursion for the variances is not specified by finite-dimensional parameters. Instead we impose nonparametric smoothness conditions. We propose a least squares estimator for this function and show that it is consistent with a rate that we conjecture to be nearly optimal.

Keywords:

• INGARCH
• nonparametric least squares
• empirical process
• mixing

AMS Subject Classifications:

• 62G20
• 62M10

Acknowledgments

MW thanks Florian Wechsung for revising the manuscript and giving some valuable comments.

Disclosure statement

No potential conflict of interest was reported by the author(s).