Estimation in a class of nonlinear heteroscedastic time series models

TL;DR

This paper studies parameter estimation in nonlinear heteroscedastic time series models, proving estimator properties, defining kernel estimators for noise density, and demonstrating good performance through simulations.

Contribution

It establishes the existence, consistency, and asymptotic normality of estimators, and introduces kernel estimators for noise density in heteroscedastic models.

Findings

Estimators are consistent and asymptotically normal.

Kernel estimators are uniformly consistent.

Simulation shows good estimator performance for large samples.

Abstract

Parameter estimation in a class of heteroscedastic time series models is investigated. The existence of conditional least-squares and conditional likelihood estimators is proved. Their consistency and their asymptotic normality are established. Kernel estimators of the noise's density and its derivatives are defined and shown to be uniformly consistent. A simulation experiment conducted shows that the estimators perform well for large sample size.