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

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  • Boubacar Mainassara, Yacouba
  • Francq, Christian

Abstract

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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Keywords: Echelon form; Lagrange Multiplier test; Likelihood Ratio test; Nonlinear processes; QMLE; Structural representation; VARMA models; Wald test.;

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  1. Francq, Christian & Zakoïan, Jean-Michel, 2007. "HAC estimation and strong linearity testing in weak ARMA models," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 98(1), pages 114-144, January.
  2. Duchesne, Pierre & Roy, Roch, 2004. "On consistent testing for serial correlation of unknown form in vector time series models," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 89(1), pages 148-180, April.
  3. 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.
  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, Elsevier, vol. 118(1-2), pages 151-187.
  5. 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, American Statistical Association, vol. 100, pages 532-544, June.
  6. Kohn, R, 1979. "Asymptotic Estimation and Hypothesis Testing Results for Vector Linear Time Series Models," Econometrica, Econometric Society, Econometric Society, vol. 47(4), pages 1005-30, July.
  7. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, Econometric Society, vol. 59(3), pages 817-58, May.
  8. Francq, Christian & Zako an, Jean-Michel, 2000. "Estimating Weak Garch Representations," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 16(05), pages 692-728, October.
  9. Nsiri, Saïd & Roy, Roch, 1996. "Identification of Refined ARMA Echelon Form Models for Multivariate Time Series," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 56(2), pages 207-231, February.
  10. 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.
  11. Hannan, E. J. & Dunsmuir, W. T. M. & Deistler, M., 1980. "Estimation of vector ARMAX models," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 10(3), pages 275-295, September.
  12. Christian Kascha, 2007. "A Comparison of Estimation Methods for Vector Autoregressive Moving-Average Models," Economics Working Papers, European University Institute ECO2007/12, European University Institute.
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Cited by:
  1. Tucker McElroy & Michael W. McCracken, 2012. "Multi-step ahead forecasting of vector time series," Working Papers, Federal Reserve Bank of St. Louis 2012-060, Federal Reserve Bank of St. Louis.
  2. Boubacar Mainassara, Yacouba, 2009. "Multivariate portmanteau test for structural VARMA models with uncorrelated but non-independent error terms," MPRA Paper 18990, University Library of Munich, Germany.

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