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.
Highlights
The class of vector autoregressive moving-average (VARMA) models and the sub-class of vector autoregressive (VAR) models are used in time series analysis and econometrics to describe the properties of the individual time series and the possible cross-relationships between the time series
This paper is devoted to the problems of computing and estimating the asymptotic variance matrix of the least squares (LS) and/or the quasi-maximum likelihood (QML) estimators of VARMA models under the assumption that the errors are uncorrelated but not necessarily independent
Such nonlinearities may arise for instance when the error process follows an autoregressive conditional heteroscedasticity (ARCH) introduced by Engle [18] and extended to the generalized ARCH (GARCH) by [5], all-pass or other models displaying a second order dependence
Summary
The class of vector autoregressive moving-average (VARMA) models and the sub-class of vector autoregressive (VAR) models are used in time series analysis and econometrics to describe the properties of the individual time series and the possible cross-relationships between the time series (see [36, 41]). This paper is devoted to the problems of computing and estimating the asymptotic variance matrix of the least squares (LS) and/or the quasi-maximum likelihood (QML) estimators of VARMA models under the assumption that the errors are uncorrelated but not necessarily independent. These models are called weak VARMA in contrast to the standard VARMA models, called strong VARMA models, in which the error terms are supposed to be independent and identically distributed (iid). Let 0r be the null vector of Rr, and let Ir be the r × r identity matrix
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
