IDEAS home Printed from https://ideas.repec.org/p/ulb/ulbeco/2013-13754.html
   My bibliography  Save this paper

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

Author

Listed:
  • Guy Melard
  • Roch Roy
  • Abdessamad Saidi

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.

Suggested Citation

  • Guy Melard & Roch Roy & Abdessamad Saidi, 2006. "Exact maximum likelihood estimation of structured or unit root multivariate time series models," ULB Institutional Repository 2013/13754, ULB -- Universite Libre de Bruxelles.
    • Handle: RePEc:ulb:ulbeco:2013/13754
    Note: SCOPUS: ar.j
    as

    Download full text from publisher

    File URL: https://dipot.ulb.ac.be/dspace/bitstream/2013/13754/2/paper_CSDA042505.pdf
    File Function: paper_CSDA042505
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. DUFOUR, Jean-Marie & JOUINI, Tarek, 2005. "Asymptotic Distribution of a Simple Linear Estimator for VARMA Models in Echelon Form," Cahiers de recherche 10-2005, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    2. 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.
    3. B. L. Shea, 1989. "The Exact Likelihood of a Vector Autoregressive Moving Average Model," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 38(1), pages 161-184, March.
    4. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 39(3), pages 106-135.
    5. Poskitt, D. & Lütkepohl, H., 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.
    6. 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.
    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. José Alberto Mauricio, 2002. "An algorithm for the exact likelihood of a stationary vector autoregressive‐moving average model," Journal of Time Series Analysis, Wiley Blackwell, vol. 23(4), pages 473-486, July.
    10. G. Gardner & A. C. Harvey & G. D. A. Phillips, 1980. "An Algorithm for Exact Maximum Likelihood Estimation of Autoregressive–Moving Average Models by Means of Kaiman Filtering," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 29(3), pages 311-322, November.
    11. 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.
    12. 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.
    13. Solo, Victor, 1984. "The exact likelihood for a multivariate ARMA model," Journal of Multivariate Analysis, Elsevier, vol. 15(2), pages 164-173, October.
    14. 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.
    15. Piero Barone, 1987. "A METHOD FOR GENERATING INDEPENDENT REALIZATIONS OF A MULTIVARIATE NORMAL STATIONARY AND INVERTIBLE ARMA(p, q) PROCESS," Journal of Time Series Analysis, Wiley Blackwell, vol. 8(2), pages 125-130, March.
    16. Ruey S. Tsay, 1989. "Identifying Multivariate Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 10(4), pages 357-372, July.
    17. B. L. Shea, 1987. "Estimation Of Multivariate Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 8(1), pages 95-109, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. Marie-Christine Duker & David S. Matteson & Ruey S. Tsay & Ines Wilms, 2024. "Vector AutoRegressive Moving Average Models: A Review," Papers 2406.19702, arXiv.org.
    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. 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.
    6. 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.
    7. Guy Melard, 2020. "An Indirect Proof for the Asymptotic Properties of VARMA Model Estimators," Working Papers ECARES 2020-10, ULB -- Universite Libre de Bruxelles.
    8. Jean-Marie Dufour & Tarek Jouini, 2011. "Asymptotic Distributions for Some Quasi-Efficient Estimators in Echelon VARMA Models," CIRANO Working Papers 2011s-25, CIRANO.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. Marie-Christine Duker & David S. Matteson & Ruey S. Tsay & Ines Wilms, 2024. "Vector AutoRegressive Moving Average Models: A Review," Papers 2406.19702, arXiv.org.
    3. 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.
    4. Mauricio, Jose Alberto, 2008. "Computing and using residuals in time series models," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1746-1763, January.
    5. Mauricio, Jose Alberto, 2006. "Exact maximum likelihood estimation of partially nonstationary vector ARMA models," Computational Statistics & Data Analysis, Elsevier, vol. 50(12), pages 3644-3662, August.
    6. Lütkepohl, Helmut, 1999. "Vector autoregressive analysis," SFB 373 Discussion Papers 1999,31, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    7. Lütkepohl, Helmut, 1999. "Vector autoregressions," SFB 373 Discussion Papers 1999,4, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    8. 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.
    9. Lütkepohl,Helmut & Krätzig,Markus (ed.), 2004. "Applied Time Series Econometrics," Cambridge Books, Cambridge University Press, number 9780521547871.
    10. George Athanasopoulos & D. Poskitt & Farshid Vahid, 2012. "Two Canonical VARMA Forms: Scalar Component Models Vis-à-Vis the Echelon Form," Econometric Reviews, Taylor & Francis Journals, vol. 31(1), pages 60-83.
    11. Cribari-Neto, Francisco, 1996. "On time series econometrics," The Quarterly Review of Economics and Finance, Elsevier, vol. 36(Supplemen), pages 37-60.
    12. Bhansali, Rajendra J., 2020. "Model specification and selection for multivariate time series," Journal of Multivariate Analysis, Elsevier, vol. 175(C).
    13. 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.
    14. D. S. Poskitt & M. O. Salau, 1995. "On The Relationship Between Generalized Least Squares And Gaussian Estimation Of Vector Arma Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(6), pages 617-645, November.
    15. Rajae Azrak & Guy Melard, 1998. "The exact quasi-likelihood of time dependent ARMA models," ULB Institutional Repository 2013/13740, ULB -- Universite Libre de Bruxelles.
    16. Dufour, Jean-Marie & Jouini, Tarek, 2014. "Asymptotic distributions for quasi-efficient estimators in echelon VARMA models," Computational Statistics & Data Analysis, Elsevier, vol. 73(C), pages 69-86.
    17. Pierre Duchesne, 2005. "Testing for serial correlation of unknown form in cointegrated time series models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(3), pages 575-595, September.
    18. Yu‐Pin Hu & Rouh‐Jane Chou, 2004. "On The Peña–Box Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(6), pages 811-830, November.
    19. Herwartz, Helmut & Reimers, Hans-Eggert, 2006. "Modelling the Fisher hypothesis: World wide evidence," Economics Working Papers 2006-04, Christian-Albrechts-University of Kiel, Department of Economics.
    20. Bilal Mehmood & Syed Hassan Raza & Mahwish Rana & Huma Sohaib & Muhammad Azhar Khan, 2014. "Triangular Relationship between Energy Consumption, Price Index and National Income in Asian Countries: A Pooled Mean Group Approach in Presence of Structural Breaks," International Journal of Energy Economics and Policy, Econjournals, vol. 4(4), pages 610-620.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ulb:ulbeco:2013/13754. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Benoit Pauwels (email available below). General contact details of provider: https://edirc.repec.org/data/ecsulbe.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.