Asymptotic behavior of the Laplacian quasi-maximum likelihood estimator of affine causal processes

TL;DR

This paper establishes the consistency and asymptotic normality of the Laplacian QMLE for a broad class of causal time series models, highlighting its robustness and advantages over Gaussian QMLE, supported by numerical simulations.

Contribution

It introduces and analyzes the Laplacian QMLE for various causal processes, demonstrating its theoretical properties and practical benefits over traditional methods.

Findings

Laplacian QMLE is consistent and asymptotically normal.

It offers robustness and higher moment order advantages.

Numerical simulations confirm estimator accuracy.

Abstract

We prove the consistency and asymptotic normality of the Laplacian Quasi-Maximum Likelihood Estimator (QMLE) for a general class of causal time series including ARMA, AR($\infty$), GARCH, ARCH($\infty$), ARMA-GARCH, APARCH, ARMA-APARCH,..., processes. We notably exhibit the advantages (moment order and robustness) of this estimator compared to the classical Gaussian QMLE. Numerical simulations confirms the accuracy of this estimator.