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

TL;DR

This paper introduces a nonparametric least squares estimator for integer-valued GARCH models, demonstrating its consistency and near-optimal convergence rate under smoothness conditions.

Contribution

It develops a nonparametric estimation method for the link function in integer-valued GARCH models, extending the modeling flexibility beyond parametric forms.

Findings

The estimator is consistent under smoothness assumptions.

The convergence rate of the estimator is nearly optimal.

The approach broadens the applicability of GARCH models to count data.

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, but 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.