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Shrinkage estimation for multivariate Hidden Markov Models
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Fiecas, Mark, Franke, Jürgen, von Sachs, Rainer and Tadjuidje Kamgaing, Joseph (2017) Shrinkage estimation for multivariate Hidden Markov Models. Journal of the American Statistical Association, 112 (517). pp. 424-435. doi:10.1080/01621459.2016.1148608 ISSN 0162-1459.
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Official URL: http://dx.doi.org/10.1080/01621459.2016.1148608
Abstract
Motivated from a changing market environment over time, we consider high-dimensional data such as financial returns, generated by a hidden Markov model that allows for switching between different regimes or states. To get more stable estimates of the covariance matrices of the different states, potentially driven by a number of observations which is small compared to the dimension, we modify the EM algorithm so that it yields the shrinkage estimators for the covariance matrices. The final algorithm turns out to reproduce better estimates not only for the covariance matrices but also for the transition matrix. It results into a more stable and reliable filter that allows for reconstructing the values of the hidden Markov chain. In addition to a simulation study performed in this paper, we also present a series of theoretical results that includes dimensionality asymptotics and provide the motivation for certain techniques used in the algorithm.
Item Type: | Journal Article | ||||||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||||
Journal or Publication Title: | Journal of the American Statistical Association | ||||||||||
Publisher: | American Statistical Association | ||||||||||
ISSN: | 0162-1459 | ||||||||||
Official Date: | 2017 | ||||||||||
Dates: |
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Volume: | 112 | ||||||||||
Number: | 517 | ||||||||||
Page Range: | pp. 424-435 | ||||||||||
DOI: | 10.1080/01621459.2016.1148608 | ||||||||||
Status: | Peer Reviewed | ||||||||||
Publication Status: | Published | ||||||||||
Access rights to Published version: | Restricted or Subscription Access |
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