A hierarchical approach to covariance function estimation for time series (Q2740034)

In the context of multivariate analysis, \textit{M.J. Daniels} and \textit{R.E. Kass} [J. Am. Stat. Assoc. 94, No. 448, 1254-1263 (1999)] discussed the idea of borrowing strength from a structured covariance matrix to obtain a stable estimate of covariances in small samples. Their approach allows the data to determine the amount of shrinkage towards this structure. As a result, the uncertainty in the knowledge of the true structure is incorporated into the variability of the estimate and precision is gained over the standard unshrunken estimate.NEWLINENEWLINENEWLINEThe intention in this paper is to extend this approach to the context of time series modeling and prediction. Thus, instead of fitting a specific parametric model to the covariance function, a methodology for shrinkage towards a parametric model is developed. This approach can be thought of as a means to smooth or shrink the spectral density towards a particular parametric form for the density. This approach is computationally tenable using the approximate model (computationally, this only requires inversion of one \(n\times n\) covariance matrix).