Physical Sciences and Mathematics 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 …

Time series data obtained from neurophysiological signals is often high-dimensional and the length of the time series is often short relative to the number of dimensions. Thus, it is difficult or sometimes impossible to compute statistics that are based on the spectral density matrix because these matrices are numerically unstable. In this work, we discuss the importance of regularization for spectral analysis of high-dimensional time series and propose shrinkage estimation for estimating high-dimensional spectral density matrices. The shrinkage estimator is derived from a penalized log-likelihood, and the optimal penalty parameter has a closed-form solution, which can be estimated using the …