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Estimating the Kronecker indices of cointegrated echelon form VARMA models

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  • Bartel, Holger
  • Lütkepohl, Helmut

Abstract

Cointegrated VARMA models can be parameterized by using the echelon form, which is characterized by the Kronecker indices. Three different methods for estimating the Kronecker indices of cointegrated echelon form VARMA models are discussed and compared. They have the common feature of estimating the individual equations of the system separately and using order selection criteria. The small sample performance of the methods is compared in a simulation study. It is found that the performance is better if all echelon form restrictions implied by the Kronecker indices found in preceeding steps are incorporated immediately.

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  • Bartel, Holger & Lütkepohl, Helmut, 1997. "Estimating the Kronecker indices of cointegrated echelon form VARMA models," SFB 373 Discussion Papers 1997,2, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:19972
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    1. Lutkepohl, Helmut & Claessen, Holger, 1997. "Analysis of cointegrated VARMA processes," Journal of Econometrics, Elsevier, vol. 80(2), pages 223-239, October.
    2. 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.
    3. 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.
    4. 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.
    5. Poskitt, D., 1996. "The Analysis of Cointegrated Autoregressive Moving-Average Systems," SFB 373 Discussion Papers 1996,58, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    6. 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.
    7. Sergio G. Koreisha & Tarmo Pukkila, 1993. "Determining The Order Of A Vector Autoregression When The Number Of Component Series Is Large," Journal of Time Series Analysis, Wiley Blackwell, vol. 14(1), pages 47-69, January.
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    Cited by:

    1. Marie-Christine Duker & David S. Matteson & Ruey S. Tsay & Ines Wilms, 2024. "Vector AutoRegressive Moving Average Models: A Review," Papers 2406.19702, arXiv.org.
    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. 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. Lütkepohl,Helmut & Krätzig,Markus (ed.), 2004. "Applied Time Series Econometrics," Cambridge Books, Cambridge University Press, number 9780521547871, October.
    5. 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.
    6. 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.
    7. Helmut Luetkepohl, 2007. "Econometric Analysis with Vector Autoregressive Models," Economics Working Papers ECO2007/11, European University Institute.
    8. Jean-Marie Dufour & Tarek Jouini, 2011. "Asymptotic Distributions for Some Quasi-Efficient Estimators in Echelon VARMA Models," CIRANO Working Papers 2011s-25, CIRANO.

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