Optimal estimation of time series functions

The principal methods of spectral estimation include kernel smoothing, ME-AR methods, and the Prony algorithm. In this paper we consider not only the estimation of spectral density matrices, but also related time series functions such as transfer functions, gain, phase, cepstrum, and so on. Computational algorithms are developed for use of splines as estimators. Smoothing splines are shown to be special cases of kernel smoothers so that properties of kernel smoothers carry over to spline estimators. Optimality of these estimators is discussed.