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

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Author Info
Boubacar Mainassara, Yacouba
Francq, Christian

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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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File URL: http://mpra.ub.uni-muenchen.de/15141/
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Publisher Info
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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Related research
Keywords: Echelon form; Lagrange Multiplier test; Likelihood Ratio test; Nonlinear processes; QMLE; Structural representation; VARMA models; Wald test.;

Find related papers by JEL classification:
C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. 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. [Downloadable!] (restricted)
  2. 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. [Downloadable!] (restricted)
  3. Christian Francq & Hamdi Raïssi, 2007. "Multivariate Portmanteau Test For Autoregressive Models with Uncorrelated but Nonindependent Errors," Journal of Time Series Analysis, Blackwell Publishing, vol. 28(3), pages 454-470, 05. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
  5. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May. [Downloadable!] (restricted)
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  6. Christian Kascha, 2007. "A Comparison of Estimation Methods for Vector Autoregressive Moving-Average Models," Economics Working Papers ECO2007/12, European University Institute. [Downloadable!]
  7. 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. [Downloadable!] (restricted)
  8. 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. [Downloadable!] (restricted)
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This page was last updated on 2009-11-10.

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