IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v100y2009i3p397-421.html
   My bibliography  Save this article

Estimating ARMAX systems for multivariate time series using the state approach to subspace algorithms

Author

Listed:
  • Bauer, Dietmar

Abstract

This paper discusses the asymptotic properties of estimators of ARMAX systems under weak low-level assumptions on the joint input/output process. The prime representative of this class of algorithms is CVA [W.E. Larimore, System identification, reduced order filters and modeling via canonical variate analysis, in: H.S. Rao, P. Dorato (Eds.), Proc. 1983 Amer. Control Conference 2, Piscataway, NJ, 1983, pp. 445-451]. Sufficient assumptions for strong consistency of the transfer function estimators under the assumption of correct specification are derived and explicit bounds on the orders of convergence are given. The assumptions used on the exogenous inputs are considerably weaker than the ones used in the results available in the literature typically requiring the inputs to be ARMA processes themselves, such as is assumed e.g. in [K. Peternell, W. Scherrer, M. Deistler, Statistical analysis of novel subspace identification methods, Signal Processing 52 (1996) 161-177]. Further sufficient conditions for the asymptotic normality of the estimated parameters are given, again under the assumption of correct specification. Finally two order estimation methods are analyzed and conditions for their consistency are derived.

Suggested Citation

  • Bauer, Dietmar, 2009. "Estimating ARMAX systems for multivariate time series using the state approach to subspace algorithms," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 397-421, March.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:3:p:397-421
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(08)00148-6
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Bauer, Dietmar, 2005. "Estimating Linear Dynamical Systems Using Subspace Methods," Econometric Theory, Cambridge University Press, vol. 21(1), pages 181-211, February.
    2. Silvia Gonçalves & Lutz Kilian, 2003. "Asymptotic and Bootstrap Inference for AR( Infinite ) Processes with Conditional Heteroskedasticity," CIRANO Working Papers 2003s-28, CIRANO.
    3. Camba-Méndez, Gonzalo & Kapetanios, George, 2001. "Testing the rank of the Hankel matrix: a statistical approach," Working Paper Series 45, European Central Bank.
    4. Kuersteiner, Guido M., 2005. "Automatic Inference For Infinite Order Vector Autoregressions," Econometric Theory, Cambridge University Press, vol. 21(1), pages 85-115, February.
    5. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    6. Dietmar Bauer, 2005. "Comparing the CCA Subspace Method to Pseudo Maximum Likelihood Methods in the case of No Exogenous Inputs," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(5), pages 631-668, September.
    Full references (including those not matched with items on IDEAS)

    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. Christian Kascha, 2012. "A Comparison of Estimation Methods for Vector Autoregressive Moving-Average Models," Econometric Reviews, Taylor & Francis Journals, vol. 31(3), pages 297-324.
    2. Alfredo García‐Hiernaux, 2011. "Forecasting linear dynamical systems using subspace methods," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(5), pages 462-468, September.
    3. Bauer, Dietmar, 2008. "Using Subspace Methods For Estimating Arma Models For Multivariate Time Series With Conditionally Heteroskedastic Innovations," Econometric Theory, Cambridge University Press, vol. 24(4), pages 1063-1092, August.
    4. 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.
    5. Antonio Rubia & Trino-Manuel Ñíguez, 2006. "Forecasting the conditional covariance matrix of a portfolio under long-run temporal dependence," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(6), pages 439-458.
    6. Jonas Mockus, 2010. "On simulation of optimal strategies and Nash equilibrium in the financial market context," Journal of Global Optimization, Springer, vol. 48(1), pages 129-143, September.
    7. Claudio Morana, 2010. "Heteroskedastic Factor Vector Autoregressive Estimation of Persistent and Non Persistent Processes Subject to Structural Breaks," ICER Working Papers - Applied Mathematics Series 36-2010, ICER - International Centre for Economic Research.
    8. Claudio Morana, 2014. "Factor Vector Autoregressive Estimation of Heteroskedastic Persistent and Non Persistent Processes Subject to Structural Breaks," Working Papers 273, University of Milano-Bicocca, Department of Economics, revised May 2014.
    9. Goncalves, Silvia & Kilian, Lutz, 2004. "Bootstrapping autoregressions with conditional heteroskedasticity of unknown form," Journal of Econometrics, Elsevier, vol. 123(1), pages 89-120, November.
    10. Luis Gil-Alana, 2004. "Forecasting the real output using fractionally integrated techniques," Applied Economics, Taylor & Francis Journals, vol. 36(14), pages 1583-1589.
    11. Nielsen, Morten Orregaard & Shimotsu, Katsumi, 2007. "Determining the cointegrating rank in nonstationary fractional systems by the exact local Whittle approach," Journal of Econometrics, Elsevier, vol. 141(2), pages 574-596, December.
    12. Giorgio Canarella & Luis A. Gil-Alana & Rangan Gupta & Stephen M. Miller, 2022. "Globalization, long memory, and real interest rate convergence: a historical perspective," Empirical Economics, Springer, vol. 63(5), pages 2331-2355, November.
    13. Hassler, U. & Marmol, F. & Velasco, C., 2006. "Residual log-periodogram inference for long-run relationships," Journal of Econometrics, Elsevier, vol. 130(1), pages 165-207, January.
    14. Haldrup, Niels & Nielsen, Morten Orregaard, 2006. "A regime switching long memory model for electricity prices," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 349-376.
    15. Pierre Perron & Zhongjun Qu, 2007. "An Analytical Evaluation of the Log-periodogram Estimate in the Presence of Level Shifts," Boston University - Department of Economics - Working Papers Series wp2007-044, Boston University - Department of Economics.
    16. Derek Bond & Michael J. Harrison & Edward J. O'Brien, 2005. "Testing for Long Memory and Nonlinear Time Series: A Demand for Money Study," Trinity Economics Papers tep20021, Trinity College Dublin, Department of Economics.
    17. Geoffrey Ngene & Ann Nduati Mungai & Allen K. Lynch, 2018. "Long-Term Dependency Structure and Structural Breaks: Evidence from the U.S. Sector Returns and Volatility," Review of Pacific Basin Financial Markets and Policies (RPBFMP), World Scientific Publishing Co. Pte. Ltd., vol. 21(02), pages 1-38, June.
    18. Lee, Yoon-Jin & Okui, Ryo & Shintani, Mototsugu, 2018. "Asymptotic inference for dynamic panel estimators of infinite order autoregressive processes," Journal of Econometrics, Elsevier, vol. 204(2), pages 147-158.
    19. Youwei Li & Xue-Zhong He, 2005. "Long Memory, Heterogeneity, and Trend Chasing," Computing in Economics and Finance 2005 113, Society for Computational Economics.
    20. Ra l De Jes s Guti rrez & Lidia E. Carvajal Guti rrez & Oswaldo Garcia Salgado, 2023. "Value at Risk and Expected Shortfall Estimation for Mexico s Isthmus Crude Oil Using Long-Memory GARCH-EVT Combined Approaches," International Journal of Energy Economics and Policy, Econjournals, vol. 13(4), pages 467-480, July.

    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:eee:jmvana:v:100:y:2009:i:3:p:397-421. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.