Longitudinal Data Analysis and Time Series Commons^™

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 …