IDEAS home Printed from https://ideas.repec.org/a/bla/jtsera/v26y2005i5p631-668.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-9892.2005.00441.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1467-9892.2005.00441.x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Robinson, Peter M, 1988. "The Stochastic Difference between Econometric Statistics," Econometrica, Econometric Society, vol. 56(3), pages 531-548, May.
    2. Bauer, Dietmar & Wagner, Martin, 2002. "Estimating cointegrated systems using subspace algorithms," Journal of Econometrics, Elsevier, vol. 111(1), pages 47-84, November.
    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. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Bauer, Dietmar & Wagner, Martin, 2002. "Estimating cointegrated systems using subspace algorithms," Journal of Econometrics, Elsevier, vol. 111(1), pages 47-84, November.

    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. Mauricio, Jose Alberto, 2006. "Exact maximum likelihood estimation of partially nonstationary vector ARMA models," Computational Statistics & Data Analysis, Elsevier, vol. 50(12), pages 3644-3662, August.
    2. Linton, Oliver, 1995. "Second Order Approximation in the Partially Linear Regression Model," Econometrica, Econometric Society, vol. 63(5), pages 1079-1112, September.
    3. Guang Cheng, 2013. "How Many Iterations are Sufficient for Efficient Semiparametric Estimation?," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(3), pages 592-618, September.
    4. Haoying Wang, 2018. "Pricing used books on Amazon.com: a spatial approach to price dispersion," Spatial Economic Analysis, Taylor & Francis Journals, vol. 13(1), pages 99-117, January.
    5. Frazier, David T. & Renault, Eric, 2017. "Efficient two-step estimation via targeting," Journal of Econometrics, Elsevier, vol. 201(2), pages 212-227.
    6. Antoine, Bertille & Bonnal, Helene & Renault, Eric, 2007. "On the efficient use of the informational content of estimating equations: Implied probabilities and Euclidean empirical likelihood," Journal of Econometrics, Elsevier, vol. 138(2), pages 461-487, June.
    7. Martin Wagner, 2008. "On PPP, unit roots and panels," Empirical Economics, Springer, vol. 35(2), pages 229-249, September.
    8. Bauer, Dietmar & Wagner, Martin, 2009. "Using subspace algorithm cointegration analysis: Simulation performance and application to the term structure," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 1954-1973, April.
    9. De Luca, Giuseppe & Magnus, Jan R. & Peracchi, Franco, 2018. "Weighted-average least squares estimation of generalized linear models," Journal of Econometrics, Elsevier, vol. 204(1), pages 1-17.
    10. Bruins, Marianne & Duffy, James A. & Keane, Michael P. & Smith, Anthony A., 2018. "Generalized indirect inference for discrete choice models," Journal of Econometrics, Elsevier, vol. 205(1), pages 177-203.
    11. Segismundo Izquierdo & Ces�reo Hern�ndez & Javier Pajares, 2005. "State Space Modelling of Cointegrated Systems using Subspace Algorithms," Econometrics 0509010, University Library of Munich, Germany, revised 07 Feb 2006.
    12. Martin Wagner, 2004. "A Comparison of Johansen's, Bierens’ and the Subspace Algorithm Method for Cointegration Analysis," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 66(3), pages 399-424, July.
    13. Kasahara, Hiroyuki & Shimotsu, Katsumi, 2008. "Pseudo-likelihood estimation and bootstrap inference for structural discrete Markov decision models," Journal of Econometrics, Elsevier, vol. 146(1), pages 92-106, September.
    14. Robinson, P.M. & Vidal Sanz, J., 2006. "Modified Whittle estimation of multilateral models on a lattice," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1090-1120, May.
    15. Rilstone, Paul & Srivastava, V. K. & Ullah, Aman, 1996. "The second-order bias and mean squared error of nonlinear estimators," Journal of Econometrics, Elsevier, vol. 75(2), pages 369-395, December.
    16. Poskitt, D.S., 2016. "Vector autoregressive moving average identification for macroeconomic modeling: A new methodology," Journal of Econometrics, Elsevier, vol. 192(2), pages 468-484.
    17. Hafner C. & Linton, O., 2013. "An Almost Closed Form Estimator for the EGARCH," LIDAM Discussion Papers ISBA 2013010, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    18. Peter Robinson & J. Vidal Sanz Vidal Sanz, 2003. "Modified whittle estimation of multilateral spatial models," CeMMAP working papers CWP18/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    19. Jean-Jacques Forneron, 2023. "Noisy, Non-Smooth, Non-Convex Estimation of Moment Condition Models," Papers 2301.07196, arXiv.org, revised Feb 2023.
    20. Gupta, Abhimanyu, 2023. "Efficient closed-form estimation of large spatial autoregressions," Journal of Econometrics, Elsevier, vol. 232(1), pages 148-167.

    More about this item

    Statistics

    Access and download statistics

    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:bla:jtsera:v:26:y:2005:i:5:p:631-668. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0143-9782 .

    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.