Statistics and Probability Commons^™

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 …