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Exact maximum likelihood estimation of structured or unit root multivariate time series models

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  • Melard, Guy
  • Roy, Roch
  • Saidi, Abdessamad

Abstract

The exact likelihood function of a Gaussian vector autoregressive-moving average (VARMA) model is evaluated in two nonstandard cases: (a) a parsimonious structured form, such as obtained in the echelon form structure or the scalar component model (SCM) structure; (b) a partially nonstationary (integrated of order 1) model in error-correction form. The starting point is any algorithm for computing the exact likelihood of a Gaussian VARMA time series. Our algorithm also provides the parameter estimates and their standard errors. The small sample properties of our algorithm were studied by Monte Carlo methods. Examples with real data are provided. © 2005 Elsevier B.V. All rights reserved.
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  • Melard, Guy & Roy, Roch & Saidi, Abdessamad, 2006. "Exact maximum likelihood estimation of structured or unit root multivariate time series models," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 2958-2986, July.
  • Handle: RePEc:eee:csdana:v:50:y:2006:i:11:p:2958-2986
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    1. 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.
    2. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 39(3), pages 106-135.
    3. D. Poskitt & H. Lütkepohl, 1995. "Consistent Specification of Cointegrated Autoregressive Moving-Average Systems," SFB 373 Discussion Papers 1995,54, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    4. Reinsel, Greg, 1979. "FIML estimation of the dynamic simultaneous equations model with ARMA disturbances," Journal of Econometrics, Elsevier, vol. 9(3), pages 263-281, February.
    5. Holger Bartel & Helmut Lutkepohl, 1998. "Estimating the Kronecker indices of cointegrated echelon-form VARMA models," Econometrics Journal, Royal Economic Society, vol. 1(Conferenc), pages 76-99.
    6. DUFOUR, Jean-Marie & TAREK, Jouini, 2005. "Asymptotic Distribution of a Simple Linear Estimator for VARMA Models in Echelon Form," Cahiers de recherche 2005-09, Universite de Montreal, Departement de sciences economiques.
    7. Dinh Tuan Pham & Roch Roy & Lyne Cédras, 2003. "Tests for non-correlation of two cointegrated ARMA time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(5), pages 553-577, September.
    8. Mittnik, Stefan, 1991. "Derivation of the unconditional state-covariance matrix for exact maximum-likelihood estimation of ARMA models," Journal of Economic Dynamics and Control, Elsevier, vol. 15(4), pages 731-740, October.
    9. Ansley, Craig F. & Newbold, Paul, 1980. "Finite sample properties of estimators for autoregressive moving average models," Journal of Econometrics, Elsevier, vol. 13(2), pages 159-183, June.
    10. Tsay, Ruey S, 1989. "Parsimonious Parameterization of Vector Autoregressive Moving Average Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(3), pages 327-341, July.
    11. Solo, Victor, 1984. "The exact likelihood for a multivariate ARMA model," Journal of Multivariate Analysis, Elsevier, vol. 15(2), pages 164-173, October.
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    Cited by:

    1. Jean-Marie Dufour & Tarek Jouini, 2011. "Asymptotic Distributions for Some Quasi-Efficient Estimators in Echelon VARMA Models," CIRANO Working Papers 2011s-25, CIRANO.
    2. DUFOUR, Jean-Marie & TAREK, Jouini, 2005. "Asymptotic Distribution of a Simple Linear Estimator for VARMA Models in Echelon Form," Cahiers de recherche 2005-09, Universite de Montreal, Departement de sciences economiques.
    3. Casals, J. & García-Hiernaux, A. & Jerez, M., 2012. "From general state-space to VARMAX models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(5), pages 924-936.
    4. Alj, Abdelkamel & Jónasson, Kristján & Mélard, Guy, 2016. "The exact Gaussian likelihood estimation of time-dependent VARMA models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 633-644.
    5. Kascha, Christian & Mertens, Karel, 2009. "Business cycle analysis and VARMA models," Journal of Economic Dynamics and Control, Elsevier, vol. 33(2), pages 267-282, February.

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