State-Space Models on the Stiefel Manifold with a New Approach to Nonlinear Filtering
1
Department of Statistics, Uppsala University, P.O. Box 513, SE-75120 Uppsala, Sweden
2
Center for Data Analytics, Stockholm School of Economics, SE-11383 Stockholm, Sweden
3
Center for Operations Research and Econometrics, Université Catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium
*
Author to whom correspondence should be addressed.
Econometrics 2018, 6(4), 48; https://doi.org/10.3390/econometrics6040048
Received: 30 July 2018 / Revised: 25 November 2018 / Accepted: 10 December 2018 / Published: 12 December 2018
(This article belongs to the Special Issue Filtering)
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.
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Keywords:
state-space models; Stiefel manifold; matrix Langevin distribution; filtering; smoothing; Laplace method; dynamic factor model; cointegration
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MDPI and ACS Style
Yang, Y.; Bauwens, L. State-Space Models on the Stiefel Manifold with a New Approach to Nonlinear Filtering. Econometrics 2018, 6, 48. https://doi.org/10.3390/econometrics6040048
AMA Style
Yang Y, Bauwens L. State-Space Models on the Stiefel Manifold with a New Approach to Nonlinear Filtering. Econometrics. 2018; 6(4):48. https://doi.org/10.3390/econometrics6040048
Chicago/Turabian StyleYang, Yukai; Bauwens, Luc. 2018. "State-Space Models on the Stiefel Manifold with a New Approach to Nonlinear Filtering" Econometrics 6, no. 4: 48. https://doi.org/10.3390/econometrics6040048
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