Skip to main content
SpringerLink
Log in

Decomposition of the multi-dimensional time series identification problem

  • Stochastic Systems
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

The mathematical model of shaping filter is constructed for a stationary multidimensional time series. The identification procedure is simplified by dividing into several steps: each step results in a multidimensional filter such that the autocovariance generating function of the transformed time series has nonzero entries in only one row, one column and in the main diagonal. This decomposition allows to construct adequat models containing relatively small number of estimated parameters. The reasonable parametrizaion, in turn, contributes to the better quality of the model due to the better statistical accuracy of the parameter estimations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Box, G.E.P., Jenkins, G.M., and Reinsel, G.C., Time Series Analysis: Forecasting and Control, Englewood Cliffs: Prentice Hall, 1994.

    MATH  Google Scholar 

  2. Tiao, G.C. and Tsay, R.S., Model Specification in Multivariate Time Series, J. R. Statist. Soc., B, (1989), vol. 51, no. 2, pp. 157–213.

  3. Neumaier, A. and Schneider, T., Estimation of Parameters and Eigenmodes of Multivariate Autoregressive Models, ACM Trans. Math. Software, 2001, vol. 27, no. 1, pp. 27–57.

    Article  MATH  Google Scholar 

  4. Schneider, T. and Neumaier, A., Algorithm 808: ARfit—a Matlab Package for the Estimation of Parameters and Eigenmodes of Multivariate Autoregressive Models, ACM Trans. Math. Software, 2001, vol. 27, no. 1, pp. 58–65.

    Article  MATH  Google Scholar 

  5. Van Overschee, P. and De Moor, B., Subspace Identification for Linear Systems: Theory, Imple-Mentation, Applications, Dordrecht: Kluwer, 1996.

    Google Scholar 

  6. Jenkins, G.M. and Watts, D.G., Spectral Analysis and Its Applications, Boca Raton: Emerson-Adams Press, 2000.

    Google Scholar 

  7. Brillinger, D.R., Time Series: Data Analysis and Theory, Philadelphia: SIAM, 2001.

    MATH  Google Scholar 

  8. Klimchenko, V.V., Multivariate Time Series Analysis Software Package, Proc. III Int. Conf. “System Identification and Control Problems” SICPRO’04, Moscow, 2004, pp. 1947–1958.

  9. Youla, D.C., On the Factorization of Rational Matrices, IRE Trans. Inform. Theory, 1961, IT-7, pp. 172–189.

    Article  Google Scholar 

  10. Higham, N.J., Accuracy and Stability of Numerical Algorithms, Philadelphia: SIAM, 2002.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Automation and Control Processes, Far-Eastern Branch, Russian Academy of Sciences, Vladivostok, Russia

    V. V. Klimchenko

Authors
  1. V. V. Klimchenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © V.V. Klimchenko, 2008, published in Avtomatika i Telemekhanika, 2008, No. 5, pp. 120–134.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Klimchenko, V.V. Decomposition of the multi-dimensional time series identification problem. Autom Remote Control 69, 845–857 (2008). https://doi.org/10.1134/S000511790805010X

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S000511790805010X

PACS numbers

Search

Navigation