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Estimating the system order by subspace methods

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  • García-Hiernaux, Alfredo
  • Casals, José
  • Jerez, Miguel

Abstract

This paper discusses how to determine the order of a state-space model. To do so, we start by revising existing approaches and find in them three basic shortcomings: i) some of them have a poor performance in short samples, ii) most of them are not robust and iii) none of them can accommodate seasonality. We tackle the first two issues by proposing new and refined criteria. The third issue is dealt with by decomposing the system into regular and seasonal sub-systems. The performance of all the procedures considered is analyzed through Monte Carlo simulations.

Suggested Citation

  • García-Hiernaux, Alfredo & Casals, José & Jerez, Miguel, 2007. "Estimating the system order by subspace methods," DES - Working Papers. Statistics and Econometrics. WS ws070301, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:ws070301
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    References listed on IDEAS

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    1. Casals, Jose & Sotoca, Sonia & Jerez, Miguel, 1999. "A fast and stable method to compute the likelihood of time invariant state-space models," Economics Letters, Elsevier, vol. 65(3), pages 329-337, December.
    2. Jesús Gonzalo & Jean‐Yves Pitarakis, 2002. "Lag length estimation in large dimensional systems," Journal of Time Series Analysis, Wiley Blackwell, vol. 23(4), pages 401-423, July.
    3. Ruey S. Tsay, 1989. "Identifying Multivariate Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 10(4), pages 357-372, July.
    4. Bujosa, Marcos & Garcia-Ferrer, Antonio & Young, Peter C., 2007. "Linear dynamic harmonic regression," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 999-1024, October.
    5. Bauer, Dietmar, 2005. "Estimating Linear Dynamical Systems Using Subspace Methods," Econometric Theory, Cambridge University Press, vol. 21(1), pages 181-211, February.
    6. Sergio Koreisha & Tarmo Pukkila, 1989. "Fast Linear Estimation Methods For Vector Autoregressive Moving‐Average Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 10(4), pages 325-339, July.
    7. Carl Eckart & Gale Young, 1936. "The approximation of one matrix by another of lower rank," Psychometrika, Springer;The Psychometric Society, vol. 1(3), pages 211-218, September.
    8. Gregory C. Reinsel & Sabyasachi Basu & Sook Fwe Yap, 1992. "Maximum Likelihood Estimators In The Multivariate Autoregressive Moving‐Average Model From A Generalized Least Squares Viewpoint," Journal of Time Series Analysis, Wiley Blackwell, vol. 13(2), pages 133-145, March.
    9. D. M. Cooper & E. F. Wood, 1982. "Identifying Multivariate Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 3(3), pages 153-164, May.
    10. Bengtsson, Thomas & Cavanaugh, Joseph E., 2006. "An improved Akaike information criterion for state-space model selection," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2635-2654, June.
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    Cited by:

    1. Brum-Civelli, Conrado & Garcia-Hiernaux, Alfredo, 2023. "An indicator of monetary bias for emerging and partially dollarized economies: The case of Uruguay," International Review of Economics & Finance, Elsevier, vol. 85(C), pages 206-219.
    2. Rodrigo Mulero & Alfredo Garcia-Hiernaux, 2023. "Forecasting unemployment with Google Trends: age, gender and digital divide," Empirical Economics, Springer, vol. 65(2), pages 587-605, August.

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    More about this item

    Keywords

    System order;

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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