Quasi-MLE for quadratic ARCH model with long memory

TL;DR

This paper develops and analyzes a quasi-maximum likelihood estimation method for quadratic ARCH models with long memory, establishing its consistency, asymptotic normality, and demonstrating its performance through simulations.

Contribution

It introduces a novel QMLE approach for quadratic ARCH models with long memory, proving its theoretical properties and validating with simulation results.

Findings

QMLE estimates are consistent and asymptotically normal.

The method accurately estimates the long memory parameter d.

Simulation studies confirm the effectiveness of the proposed estimation technique.

Abstract

We discuss parametric quasi-maximum likelihood estimation for quadratic ARCH process with long memory introduced in Doukhan et al. (2015) and Grublyt\.e and \v{S}karnulis (2015) with conditional variance given by a strictly positive quadratic form of observable stationary sequence. We prove consistency and asymptotic normality of the corresponding QMLE estimates, including the estimate of long memory parameter $0< d < 1/2$. A simulation study of empirical MSE is included.