State space models on special manifolds
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.
Volume (Year): 97 (2006)
Issue (Month): 6 (July)
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- Durbin, James & Koopman, Siem Jan, 2012.
"Time Series Analysis by State Space Methods,"
Oxford University Press,
edition 2, number 9780199641178, April.
- Durbin, James & Koopman, Siem Jan, 2001. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, number 9780198523543.
- Tom Doan, "undated". "SEASONALDLM: RATS procedure to create the matrices for the seasonal component of a DLM," Statistical Software Components RTS00251, Boston College Department of Economics.
- 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. Full references (including those not matched with items on IDEAS)
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