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State-Space Models on the Stiefel Manifold with a New Approach to Nonlinear Filtering

Author

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  • Yukai Yang

    (Department of Statistics, Uppsala University, P.O. Box 513, SE-75120 Uppsala, Sweden
    Center for Data Analytics, Stockholm School of Economics, SE-11383 Stockholm, Sweden)

  • Luc Bauwens

    (Center for Operations Research and Econometrics, Université Catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium)

Abstract

We develop novel multivariate state-space models wherein the latent states evolve on the Stiefel manifold and follow a conditional matrix Langevin distribution. The latent states correspond to time-varying reduced rank parameter matrices, like the loadings in dynamic factor models and the parameters of cointegrating relations in vector error-correction models. The corresponding nonlinear filtering algorithms are developed and evaluated by means of simulation experiments.

Suggested Citation

  • Yukai Yang & Luc Bauwens, 2018. "State-Space Models on the Stiefel Manifold with a New Approach to Nonlinear Filtering," Econometrics, MDPI, vol. 6(4), pages 1-22, December.
    • Handle: RePEc:gam:jecnmx:v:6:y:2018:i:4:p:48-:d:190086
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    References listed on IDEAS

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    1. Breitung, Jörg & Eickmeier, Sandra, 2011. "Testing for structural breaks in dynamic factor models," Journal of Econometrics, Elsevier, vol. 163(1), pages 71-84, July.
    2. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
    3. Marco Del Negro & Christopher Otrok, 2008. "Dynamic factor models with time-varying parameters: measuring changes in international business cycles," Staff Reports 326, Federal Reserve Bank of New York.
    4. Bierens, Herman J. & Martins, Luis F., 2010. "Time-Varying Cointegration," Econometric Theory, Cambridge University Press, vol. 26(5), pages 1453-1490, October.
    5. Chikuse, Yasuko, 2006. "State space models on special manifolds," Journal of Multivariate Analysis, Elsevier, vol. 97(6), pages 1284-1294, July.
    6. Castle, Jennifer & Shephard, Neil (ed.), 2009. "The Methodology and Practice of Econometrics: A Festschrift in Honour of David F. Hendry," OUP Catalogue, Oxford University Press, number 9780199237197.
    7. Stock J.H. & Watson M.W., 2002. "Forecasting Using Principal Components From a Large Number of Predictors," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1167-1179, December.
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    Cited by:

    1. Niko Hauzenberger & Michael Pfarrhofer & Luca Rossini, 2020. "Sparse time-varying parameter VECMs with an application to modeling electricity prices," Papers 2011.04577, arXiv.org, revised Apr 2023.
    2. Yang, Yuhong, 2000. "Combining Different Procedures for Adaptive Regression," Journal of Multivariate Analysis, Elsevier, vol. 74(1), pages 135-161, July.

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    More about this item

    Keywords

    state-space models; Stiefel manifold; matrix Langevin distribution; filtering; smoothing; Laplace method; dynamic factor model; cointegration;
    All these keywords.

    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

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