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Estimating structural VARMA models with uncorrelated but non-independent error terms

  • Boubacar Mainassara, Yacouba
  • Francq, Christian

The asymptotic properties of the quasi-maximum likelihood estimator (QMLE) of vector autoregressive moving-average (VARMA) models are derived under the assumption that the errors are uncorrelated but not necessarily independent. Relaxing the independence assumption considerably extends the range of application of the VARMA models, and allows to cover linear representations of general nonlinear processes. Conditions are given for the consistency and asymptotic normality of the QMLE. A particular attention is given to the estimation of the asymptotic variance matrix, which may be very different from that obtained in the standard framework. Modified versions of the Wald, Lagrange Multiplier and Likelihood Ratio tests are proposed for testing linear restrictions on the parameters.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 15141.

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Date of creation: 2009
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Handle: RePEc:pra:mprapa:15141
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  1. Francq, Christian & Roy, Roch & Zakoian, Jean-Michel, 2005. "Diagnostic Checking in ARMA Models With Uncorrelated Errors," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 532-544, June.
  2. Christian Francq & Jean-Michel Zakoïan, 1997. "Estimating Weak Garch Representations," Working Papers 97-40, Centre de Recherche en Economie et Statistique.
  3. Donald W.K. Andrews, 1988. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Cowles Foundation Discussion Papers 877R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1989.
  4. Findley, David F. & Potscher, Benedikt M. & Wei, Ching-Zong, 2004. "Modeling of time series arrays by multistep prediction or likelihood methods," Journal of Econometrics, Elsevier, vol. 118(1-2), pages 151-187.
  5. Nsiri, Saïd & Roy, Roch, 1996. "Identification of Refined ARMA Echelon Form Models for Multivariate Time Series," Journal of Multivariate Analysis, Elsevier, vol. 56(2), pages 207-231, February.
  6. Christian Francq & Hamdi Raïssi, 2007. "Multivariate Portmanteau Test For Autoregressive Models with Uncorrelated but Nonindependent Errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(3), pages 454-470, 05.
  7. Christian Kascha, 2007. "A Comparison of Estimation Methods for Vector Autoregressive Moving-Average Models," Economics Working Papers ECO2007/12, European University Institute.
  8. Duchesne, Pierre & Roy, Roch, 2004. "On consistent testing for serial correlation of unknown form in vector time series models," Journal of Multivariate Analysis, Elsevier, vol. 89(1), pages 148-180, April.
  9. Hannan, E. J. & Dunsmuir, W. T. M. & Deistler, M., 1980. "Estimation of vector ARMAX models," Journal of Multivariate Analysis, Elsevier, vol. 10(3), pages 275-295, September.
  10. Whitney K. Newey & Kenneth D. West, 1986. "A Simple, Positive Semi-Definite, Heteroskedasticity and AutocorrelationConsistent Covariance Matrix," NBER Technical Working Papers 0055, National Bureau of Economic Research, Inc.
  11. Kohn, R, 1979. "Asymptotic Estimation and Hypothesis Testing Results for Vector Linear Time Series Models," Econometrica, Econometric Society, vol. 47(4), pages 1005-30, July.
  12. Francq, Christian & Zakoïan, Jean-Michel, 2007. "HAC estimation and strong linearity testing in weak ARMA models," Journal of Multivariate Analysis, Elsevier, vol. 98(1), pages 114-144, January.
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