Shrinkage Estimation for Multivariate Hidden Markov Mixture Models
(2012) , 24 + 8 pages
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Details
- Authors
- Abstract
- Motivated from a changing market environment over time, we consider high-dimensional data such as financial returns, generated by a hidden Markov model which 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 apply shrinkage and combine it with an EM-type algorithm. This approach will yield better estimates a more stable estimates of the covariance matrix, which allows for improved reconstruction of the hidden Markov chain. In addition to a simulation study and the analysis of a portfolio data set, we present a series of theoretical results which include a dimensionality asymptotics and which provide the motivation and theoretical foundation for certain techniques used by our method.
- Affiliations
University of California at San Diego Department of Psychiatry University of Kaiserslautern, Germany Department of Mathematics
Citations
Fiecas, M., Franke, J., von Sachs, R., & Tadjuidje, J. (2012). Shrinkage Estimation for Multivariate Hidden Markov Mixture Models (ISBA Discussion Paper 2012/16). https://hdl.handle.net/2078.5/208320