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Estimating the dimension of a linear system

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  • 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
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    Citations

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    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. 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.
    3. 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.
    4. Jean-Marie Dufour & Tarek Jouini, 2011. "Asymptotic Distributions for Some Quasi-Efficient Estimators in Echelon VARMA Models," CIRANO Working Papers 2011s-25, CIRANO.
    5. 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).
    6. 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.
    7. 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.
    8. Perez, Marcos & Ahn, Seung Chan, 2007. "GMM Estimation of the Number of Latent Factors," MPRA Paper 4862, University Library of Munich, Germany.
    9. 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.
    10. Cragg, John G. & Donald, Stephen G., 1997. "Inferring the rank of a matrix," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 223-250.
    11. 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.
    12. Emre Kahraman & Gazanfer Unal, 2016. "Multiple Wavelet Coherency Analysis and Forecasting of Metal Prices," Papers 1602.01960, arXiv.org.

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