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

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  • Boubacar Mainassara, Y.
  • Francq, C.

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 nor martingale differences. Relaxing the martingale difference assumption on the errors considerably extends the range of application of the VARMA models, and allows one to cover linear representations of general nonlinear processes. Conditions are given for the asymptotic normality of the QMLE. Particular attention is given to the estimation of the asymptotic variance matrix, which may be very different from that obtained in the standard framework.

Suggested Citation

  • Boubacar Mainassara, Y. & Francq, C., 2011. "Estimating structural VARMA models with uncorrelated but non-independent error terms," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 496-505, March.
  • Handle: RePEc:eee:jmvana:v:102:y:2011:i:3:p:496-505
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    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.
    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.
    3. Bénédicte Vidaillet & V. D'Estaintot & P. Abécassis, 2005. "Introduction," Post-Print hal-00287137, HAL.
    4. 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, May.
    5. 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.
    6. Francq, Christian & Zako an, Jean-Michel, 2000. "Estimating Weak Garch Representations," Econometric Theory, Cambridge University Press, vol. 16(05), pages 692-728, October.
    7. Christian Kascha, 2007. "A Comparison of Estimation Methods for Vector Autoregressive Moving-Average Models," Economics Working Papers ECO2007/12, European University Institute.
    8. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    9. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 33(1), pages 125-132.
    10. 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.
    11. Kohn, R, 1979. "Asymptotic Estimation and Hypothesis Testing Results for Vector Linear Time Series Models," Econometrica, Econometric Society, vol. 47(4), pages 1005-1030, July.
    12. 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.
    13. 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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    Citations

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    Cited by:

    1. 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.
    2. Brüggemann, Ralf & Jentsch, Carsten & Trenkler, Carsten, 2016. "Inference in VARs with conditional heteroskedasticity of unknown form," Journal of Econometrics, Elsevier, vol. 191(1), pages 69-85.
    3. Pierre Duchesne & Pierre Lafaye de Micheaux, 2013. "Distributions for residual autocovariances in parsimonious periodic vector autoregressive models with applications," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(4), pages 496-507, July.
    4. Bin Chen & Jinho Choi & Juan Carlos Escanciano, 2017. "Testing for fundamental vector moving average representations," Quantitative Economics, Econometric Society, vol. 8(1), pages 149-180, March.
    5. repec:taf:emetrv:v:36:y:2017:i:5:p:495-513 is not listed on IDEAS
    6. Tucker McElroy & Michael W. McCracken, 2017. "Multistep ahead forecasting of vector time series," Econometric Reviews, Taylor & Francis Journals, vol. 36(5), pages 495-513, May.
    7. Yacouba Boubacar Maïnassara & Célestin C. Kokonendji, 2016. "Modified Schwarz and Hannan–Quinn information criteria for weak VARMA models," Statistical Inference for Stochastic Processes, Springer, vol. 19(2), pages 199-217, July.
    8. Abdelkamel Alj & Christophe Ley & Guy Melard, 2015. "Asymptotic Properties of QML Estimators for VARMA Models with Time-Dependent Coefficients: Part I," Working Papers ECARES ECARES 2015-21, ULB -- Universite Libre de Bruxelles.
    9. Boubacar Maïnassara, Yacouba & Raïssi, Hamdi, 2015. "Semi-strong linearity testing in linear models with dependent but uncorrelated errors," Statistics & Probability Letters, Elsevier, vol. 103(C), pages 110-115.
    10. repec:bla:scjsta:v:44:y:2017:i:3:p:617-635 is not listed on IDEAS

    More about this item

    Keywords

    Asymptotic normality Nonlinear processes QMLE Structural representation VARMA models;

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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