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State space models on special manifolds

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  • Chikuse, Yasuko

Abstract

This paper concerns modeling time series observations in state space forms considered on the Stiefel and Grassmann manifolds. We develop a state space model relating the time series observations to a sequence of unobserved state or parameter matrices assuming the matrix Langevin noise processes on the Stiefel manifolds. We show a Bayes method for estimating the state matrices by the posterior modes. We consider a further extended state space model where two sequences of unobserved state matrices are involved. A simple state space model on the Grassmann manifolds with matrix Langevin noise processes is also investigated.

Suggested Citation

  • Chikuse, Yasuko, 2006. "State space models on special manifolds," Journal of Multivariate Analysis, Elsevier, vol. 97(6), pages 1284-1294, July.
    • Handle: RePEc:eee:jmvana:v:97:y:2006:i:6:p:1284-1294
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    References listed on IDEAS

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    1. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
    2. Chikuse, Y. & Watson, G. S., 1995. "Large Sample Asymptotic Theory of Tests for Uniformity on the Grassmann Manifold," Journal of Multivariate Analysis, Elsevier, vol. 54(1), pages 18-31, July.
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    Cited by:

    1. 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.

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