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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.

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  • 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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    Cited by:

    1. Mélard, Guy, 2022. "An indirect proof for the asymptotic properties of VARMA model estimators," Econometrics and Statistics, Elsevier, vol. 21(C), pages 96-111.
    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.
    3. Bernd Funovits, 2019. "Identification and Estimation of SVARMA models with Independent and Non-Gaussian Inputs," Papers 1910.04087, arXiv.org.
    4. Abdoulkarim Ilmi Amir & Yacouba Boubacar Maïnassara, 2020. "Multivariate portmanteau tests for weak multiplicative seasonal VARMA models," Statistical Papers, Springer, vol. 61(6), pages 2529-2560, December.
    5. 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.
    6. Angelini, Giovanni & Cavaliere, Giuseppe & Fanelli, Luca, 2024. "An identification and testing strategy for proxy-SVARs with weak proxies," Journal of Econometrics, Elsevier, vol. 238(2).
    7. Boubacar Mainassara, Yacouba, 2010. "Selection of weak VARMA models by modified Akaike's information criteria," MPRA Paper 24981, University Library of Munich, Germany.
    8. 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.
    9. Guy Melard, 2020. "An Indirect Proof for the Asymptotic Properties of VARMA Model Estimators," Working Papers ECARES 2020-10, ULB -- Universite Libre de Bruxelles.
    10. 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.
    11. 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.
    12. 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.
    13. Marie-Christine Duker & David S. Matteson & Ruey S. Tsay & Ines Wilms, 2024. "Vector AutoRegressive Moving Average Models: A Review," Papers 2406.19702, arXiv.org.
    14. Yacouba Boubacar Maïnassara & Youssef Esstafa & Bruno Saussereau, 2021. "Estimating FARIMA models with uncorrelated but non-independent error terms," Statistical Inference for Stochastic Processes, Springer, vol. 24(3), pages 549-608, October.
    15. 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.
    16. Abdelkamel Alj & Rajae Azrak & Christophe Ley & Guy Mélard, 2017. "Asymptotic Properties of QML Estimators for VARMA Models with Time-dependent Coefficients," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(3), pages 617-635, September.

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    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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