Asymptotic normality of the Quasi Maximum Likelihood Estimator for multidimensional causal processes

TL;DR

This paper establishes the strong consistency and asymptotic normality of the Quasi-Maximum Likelihood Estimator for a broad class of multidimensional causal processes, including new examples like TARCH and NLARCH.

Contribution

It extends existing results by weakening assumptions and provides asymptotic analysis for new classes of univariate and multivariate processes.

Findings

QMLE is strongly consistent for general multidimensional causal processes.

QMLE is asymptotically normal under weaker conditions than previous studies.

New results for TARCH and NLARCH processes.

Abstract

Strong consistency and asymptotic normality of the Quasi-Maximum Likelihood Estimator (QMLE) are given for a general class of multidimensional causal processes. For particular cases already studied in the literature (for instance univariate or multivariate GARCH, ARCH, ARMA-GARCH processes) the assumptions required for establishing these results are often weaker than existing conditions. The QMLE asymptotic behavior is also given for numerous new examples of univariate or multivariate processes (for instance TARCH or NLARCH processes).