IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v11y1981i4p459-473.html
   My bibliography  Save this article

Estimating the dimension of a linear system

Author

Listed:
  • Hannan, E. J.

Abstract

The problem considered is that of estimating the integer or integers that prescribe the dimension of a linear system. These could be the Kronecker indices. Though attention is concentrated on the order or McMillan degree, which specifies the dimension of a minimal state vector, the same results are available for other cases. A fairly complete theorem is proved relating to conditions under which strong or weak convergence will hold for an estimate of the McMillan degree when the estimation is based on minimisation of a criterion of the form log det([Omega]n) + nC(T)/T, where [Omega]n, is the estimate of the prediction error covariance matrix and the McMillan degree is assumed to be n. The conditions relate to the prescribed sequence C(T).

Suggested Citation

  • Hannan, E. J., 1981. "Estimating the dimension of a linear system," Journal of Multivariate Analysis, Elsevier, vol. 11(4), pages 459-473, December.
    • Handle: RePEc:eee:jmvana:v:11:y:1981:i:4:p:459-473
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0047-259X(81)90089-0
    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.

    Citations

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


    Cited by:

    1. Kliger, Mark & Francos, Joseph M., 2008. "Strong consistency of a family of model order selection rules for estimating 2D sinusoids in noise," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 3075-3081, December.
    2. Perez, Marcos & Ahn, Seung Chan, 2007. "GMM Estimation of the Number of Latent Factors," MPRA Paper 4862, University Library of Munich, Germany.
    3. Phillips, Peter C.B. & Ploberger, Werner, 1994. "Posterior Odds Testing for a Unit Root with Data-Based Model Selection," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 774-808, August.
    4. Emrah Oral & Gazanfer Unal, 2017. "Co-movement of precious metals and forecasting using scale by scale wavelet transform," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 1-21, March.
    5. Ahn, Seung C. & Perez, M. Fabricio, 2010. "GMM estimation of the number of latent factors: With application to international stock markets," Journal of Empirical Finance, Elsevier, vol. 17(4), pages 783-802, September.
    6. George W. Gallinger, 1994. "Causality Tests Of The Real Stock Return-Real Activity Hypothesis," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 17(2), pages 271-288, June.
    7. Cragg, John G. & Donald, Stephen G., 1997. "Inferring the rank of a matrix," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 223-250.
    8. Jean-Marie Dufour & Tarek Jouini, 2011. "Asymptotic Distributions for Some Quasi-Efficient Estimators in Echelon VARMA Models," CIRANO Working Papers 2011s-25, CIRANO.
    9. Guyon, Xavier & Yao, Jian-feng, 1999. "On the Underfitting and Overfitting Sets of Models Chosen by Order Selection Criteria," Journal of Multivariate Analysis, Elsevier, vol. 70(2), pages 221-249, August.
    10. GONZALO, Jesus & PITARAKIS, Jean-Yves, 1994. "Comovements in Large Systems," LIDAM Discussion Papers CORE 1994065, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    11. Emre Kahraman & Gazanfer Unal, 2016. "Multiple Wavelet Coherency Analysis and Forecasting of Metal Prices," Papers 1602.01960, arXiv.org.
    12. Emrah Oral & Gazanfer Unal, 2019. "Modeling and forecasting time series of precious metals: a new approach to multifractal data," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 5(1), pages 1-28, December.

    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:11:y:1981:i:4:p:459-473. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.