Open Access
2014 Estimation of the variance of the quasi-maximum likelihood estimator of weak VARMA models
Yacouba Boubacar Maïnassara
Electron. J. Statist. 8(2): 2701-2740 (2014). DOI: 10.1214/14-EJS968


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.


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Yacouba Boubacar Maïnassara. "Estimation of the variance of the quasi-maximum likelihood estimator of weak VARMA models." Electron. J. Statist. 8 (2) 2701 - 2740, 2014.


Published: 2014
First available in Project Euclid: 1 January 2015

zbMATH: 1309.62097
MathSciNet: MR3296141
Digital Object Identifier: 10.1214/14-EJS968

Primary: 62H12 , 62H15 , 62M10

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

Rights: Copyright © 2014 The Institute of Mathematical Statistics and the Bernoulli Society

Vol.8 • No. 2 • 2014
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