Electronic Journal of Statistics

Estimation of the variance of the quasi-maximum likelihood estimator of weak VARMA models

Yacouba Boubacar Maïnassara

Full-text: Open access

Abstract

This paper considers the problems of computing and estimating the asymptotic variance matrix of the least squares (LS) and/or the quasi-maximum likelihood (QML) estimators of vector autoregressive moving-average (VARMA) models under the assumption that the errors are uncorrelated but not necessarily independent. We firstly give expressions for the derivatives of the VARMA residuals in terms of the parameters of the models. Secondly we give an explicit expression of the asymptotic variance matrix of the QML/LS estimator, in terms of the VAR and MA polynomials, and of the second and fourth-order structure of the noise. We then deduce a consistent estimator of this asymptotic variance matrix. Modified versions of the Wald, Lagrange Multiplier and Likelihood Ratio tests are proposed for testing linear restrictions on the parameters. The theoretical results are illustrated by means Monte Carlo experiments.

Article information

Source
Electron. J. Statist., Volume 8, Number 2 (2014), 2701-2740.

Dates
First available in Project Euclid: 1 January 2015

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1420071973

Digital Object Identifier
doi:10.1214/14-EJS968

Mathematical Reviews number (MathSciNet)
MR3296141

Zentralblatt MATH identifier
1309.62097

Subjects
Primary: 62H12: Estimation 62H15: Hypothesis testing 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]

Keywords
Covariance matrix estimate Lagrange multiplier test likelihood ratio test QMLE/LSE residuals derivatives Wald test weak VARMA models

Citation

Boubacar Maïnassara, Yacouba. Estimation of the variance of the quasi-maximum likelihood estimator of weak VARMA models. Electron. J. Statist. 8 (2014), no. 2, 2701--2740. doi:10.1214/14-EJS968. https://projecteuclid.org/euclid.ejs/1420071973


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