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Comparing the CCA Subspace Method to Pseudo Maximum Likelihood Methods in the case of No Exogenous Inputs

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  • Dietmar Bauer

Abstract

. This paper deals with the CCA subspace algorithm proposed in Larimore [Proceeding of 1983 American Control Conference (1983) pp. 445–451], which constitutes an alternative to the classical criteria optimization based approach to the identification of linear dynamic models for a stationary process. Subspace algorithms for the estimation of linear models have been advocated mainly due to their numerical properties. A large variety of different subspace algorithms is known to provide strongly consistent and asymptotically normal estimates of the system under mild assumptions on the noise and the underlying true system. This paper shows that for certain versions of CCA described in the paper the estimates are asymptotically equivalent to pseudo maximum‐likelihood estimates in the sense that the difference in the estimators multiplied by the square root of the sample size converges to zero (in probability). Therefore these versions of CCA are asymptotically efficient for Gaussian innovations.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jtsera:v:26:y:2005:i:5:p:631-668
    DOI: 10.1111/j.1467-9892.2005.00441.x
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    References listed on IDEAS

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    1. Robinson, Peter M, 1988. "The Stochastic Difference between Econometric Statistics," Econometrica, Econometric Society, vol. 56(3), pages 531-548, May.
    2. Dahlen, Anders & Scherrer, Wolfgang, 2004. "The relation of the CCA subspace method to a balanced reduction of an autoregressive model," Journal of Econometrics, Elsevier, vol. 118(1-2), pages 293-312.
    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. Bauer, Dietmar & Wagner, Martin, 2002. "Estimating cointegrated systems using subspace algorithms," Journal of Econometrics, Elsevier, vol. 111(1), pages 47-84, November.
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    Cited by:

    1. 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.
    2. Alfredo Garcia-Hiernaux & Jose Casals & Miguel Jerez, 2024. "Identification of canonical models for vectors of time series: a subspace approach," Statistical Papers, Springer, vol. 65(3), pages 1493-1530, May.
    3. 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.
    4. 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.
    5. Bauer, Dietmar & Wagner, Martin, 2002. "Estimating cointegrated systems using subspace algorithms," Journal of Econometrics, Elsevier, vol. 111(1), pages 47-84, November.
    6. 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.
    7. 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.
    8. Izquierdo, Segismundo S. & Hernández, Cesáreo & del Hoyo, Juan, 2006. "Forecasting VARMA processes using VAR models and subspace-based state space models," MPRA Paper 4235, University Library of Munich, Germany.

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