IDEAS home Printed from https://ideas.repec.org/p/mtl/montec/10-2005.html
   My bibliography  Save this paper

Asymptotic Distribution of a Simple Linear Estimator for VARMA Models in Echelon Form

Author

Listed:
  • DUFOUR, Jean-Marie
  • JOUINI, Tarek

Abstract

In this paper, we study the asymptotic distribution of a simple two-stage (Hannan-Rissanen-type) linear estimator for stationary invertible vector autoregressive moving average (VARMA) models in the echelon form representation. General conditions for consistency and asymptotic normality are given. A consistent estimator of the asymptotic covariance matrix of the estimator is also provided, so that tests and confidence intervals can easily be constructed.

Suggested Citation

  • 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.
  • Handle: RePEc:mtl:montec:10-2005
    as

    Download full text from publisher

    File URL: http://www.cireqmontreal.com/wp-content/uploads/cahiers/10-2005-cah.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Lutkepohl, Helmut & Claessen, Holger, 1997. "Analysis of cointegrated VARMA processes," Journal of Econometrics, Elsevier, vol. 80(2), pages 223-239, October.
    3. Boudjellaba, Hafida & Dufour, Jean-Marie & Roy, Roch, 1994. "Simplified conditions for noncausality between vectors in multivariate ARMA models," Journal of Econometrics, Elsevier, vol. 63(1), pages 271-287, July.
    4. E. J. Hannan & L. Kavalieris, 1986. "Regression, Autoregression Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 7(1), pages 27-49, January.
    5. Koreisha, Sergio G & Pukkila, Tarmo, 1995. "A Comparison between Different Order-Determination Criteria for Identification of ARIMA Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(1), pages 127-131, January.
    6. Sergio Koreisha & Tarmo Pukkila, 1989. "Fast Linear Estimation Methods For Vector Autoregressive Moving‐Average Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 10(4), pages 325-339, July.
    7. 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.
    8. Lewis, Richard & Reinsel, Gregory C., 1985. "Prediction of multivariate time series by autoregressive model fitting," Journal of Multivariate Analysis, Elsevier, vol. 16(3), pages 393-411, June.
    9. Lutkepohl, Helmut & Poskitt, D S, 1996. "Specification of Echelon-Form VARMA Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 69-79, January.
    10. 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.
    11. Boudjellaba, B. & Dufour, J.M. & Roy, R., 1991. "Testing Causality Between Two Vectors in Multivariate Arma Models," Cahiers de recherche 9119, Universite de Montreal, Departement de sciences economiques.
    12. 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.
    13. Hannan, E J, 1976. "The Identification and Parameterization of ARMAX and State Space Forms," Econometrica, Econometric Society, vol. 44(4), pages 713-723, July.
    14. Deistler, M. & Hannan, E. J., 1981. "Some properties of the parameterization of ARMA systems with unknown order," Journal of Multivariate Analysis, Elsevier, vol. 11(4), pages 474-484, December.
    15. 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.
    16. D. M. Cooper & E. F. Wood, 1982. "Identifying Multivariate Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 3(3), pages 153-164, May.
    17. Paparoditis, Efstathios, 1996. "Bootstrapping Autoregressive and Moving Average Parameter Estimates of Infinite Order Vector Autoregressive Processes," Journal of Multivariate Analysis, Elsevier, vol. 57(2), pages 277-296, May.
    18. 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.
    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. 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 & Jouini, Tarek, 2014. "Asymptotic distributions for quasi-efficient estimators in echelon VARMA models," Computational Statistics & Data Analysis, Elsevier, vol. 73(C), pages 69-86.
    3. Dias, Gustavo Fruet & Kapetanios, George, 2018. "Estimation and forecasting in vector autoregressive moving average models for rich datasets," Journal of Econometrics, Elsevier, vol. 202(1), pages 75-91.
    4. 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.
    5. Dufour, Jean-Marie & Taamouti, Abderrahim, 2010. "Short and long run causality measures: Theory and inference," Journal of Econometrics, Elsevier, vol. 154(1), pages 42-58, January.
    6. Dias, Gustavo Fruet, 2017. "The time-varying GARCH-in-mean model," Economics Letters, Elsevier, vol. 157(C), pages 129-132.

    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. 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.
    4. Dufour, Jean-Marie & Taamouti, Abderrahim, 2010. "Short and long run causality measures: Theory and inference," Journal of Econometrics, Elsevier, vol. 154(1), pages 42-58, January.
    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. Lütkepohl,Helmut & Krätzig,Markus (ed.), 2004. "Applied Time Series Econometrics," Cambridge Books, Cambridge University Press, number 9780521547871, January.
    7. 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.
    8. Dufour, Jean-Marie & Tessier, David, 1997. "La causalité entre la monnaie et le revenu : une analyse fondée sur un modèle VARMA-échelon," L'Actualité Economique, Société Canadienne de Science Economique, vol. 73(1), pages 351-366, mars-juin.
    9. 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.
    10. 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.
    11. 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.
    12. Helmut Luetkepohl, 2007. "Econometric Analysis with Vector Autoregressive Models," Economics Working Papers ECO2007/11, European University Institute.
    13. Gil-Alana, Luis A. & Gupta, Rangan & Olubusoye, Olusanya E. & Yaya, OlaOluwa S., 2016. "Time series analysis of persistence in crude oil price volatility across bull and bear regimes," Energy, Elsevier, vol. 109(C), pages 29-37.
    14. 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.
    15. Bhansali, Rajendra J., 2020. "Model specification and selection for multivariate time series," Journal of Multivariate Analysis, Elsevier, vol. 175(C).
    16. 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.
    17. Yuanyuan Li & Dietmar Bauer, 2020. "Modeling I(2) Processes Using Vector Autoregressions Where the Lag Length Increases with the Sample Size," Econometrics, MDPI, vol. 8(3), pages 1-28, September.
    18. Dufour, Jean-Marie & Pelletier, Denis & Renault, Eric, 2006. "Short run and long run causality in time series: inference," Journal of Econometrics, Elsevier, vol. 132(2), pages 337-362, June.
    19. McKenzie, C.R., 1997. "The properties of some two step estimators of ARMA Models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 43(3), pages 451-456.
    20. Chan, Joshua C.C. & Eisenstat, Eric & Koop, Gary, 2016. "Large Bayesian VARMAs," Journal of Econometrics, Elsevier, vol. 192(2), pages 374-390.

    More about this item

    Keywords

    time series; VARMA; stationary; invertible; echelon form; estimation; asymptotic normality; bootstrap; Hannan-Rissanen;
    All these keywords.

    JEL classification:

    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • 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
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

    Statistics

    Access and download statistics

    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:mtl:montec:10-2005. 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: Sharon BREWER (email available below). General contact details of provider: https://edirc.repec.org/data/cdmtlca.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.