Shrinkage Estimation for Multivariate Hidden Markov Mixture Models
(2017) Journal of the American Statistical Association — Vol. 112, n° 517, p. 424-435 (2017)
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- 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.
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Citations
Fiecas, M., Franke, J., von Sachs, R., & Tadjuidje, J. (2017). Shrinkage Estimation for Multivariate Hidden Markov Mixture Models. Journal of the American Statistical Association, 112(517), 424-435. https://doi.org/10.1080/01621459.2016.1148608 (Original work published 2017)