Abstract

This paper develops the statistical procedure for the heavy-tailed vector

ARMA-GARCH model. We first study the self-weighted quasi-maximum likelihood estimator (QMLE) of the vector ARMA-GARCH model and establish its

consistency and asymptotic normality under a fractional moment condition. Using the self-weighted QMLE, we establish the asymptotic normality of the local

QMLE for VARMA model when the noise follows a finite second moment vector

GARCH or IGARCH model. Based on the two estimators, we construct the Wald

statistics for testing linear and nonlinear restrictions, and especially, we propose

a Wald statistic for testing the vector IGARCH model. We also construct two

portmanteau tests for checking the adequacy of models. All test statistics are

shown to be asymptotically χ2 distributions as the sample size goes to infinity.

Simulation results show that our procedure works well in the finite samples and

one real example is given to demonstrate how to build a model by using our

procedure.

Key words and phrases: Asymptotic normality, consistency, model checking, self- weighted QMLE, VARMA model, VGARCH model

Information

Preprint No.SS-2025-0286
Manuscript IDSS-2025-0286
Complete AuthorsBibi Cai, Mengya Liu, Shiqing Ling
Corresponding AuthorsShiqing Ling
Emailsmaling@ust.hk

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Acknowledgments

Shiqing Ling research was partially supported by Hong Kong Research

Grants Commission Grants (16303118, 16301620, 16300621, 16500522 and

Supplementary Materials

All the proofs and additional simulation results are offered in supplementary

material.

Supplementary materials are available for download.