Spectral estimation for psycho-physiological data Estimating lower-dimensional representations in frequency space

Abstract

Two different estimation techniques for the spectrum of a nonstationary time series are compared empirically. Both of them are assuming a time-dependent autoregressive (AR-) model for the data. The fifirst estimation technique used is the Frequency State Dependent Model (FSDM-) technique (Schmitz and Urfer, 1997), a modification of the well known Kalman-filter approach. The FSD-Model is based on Priestleys SD-Models for the analysis of nonstationary time series (e.g.,Priestley, 1988). An alternative approach for estimating AR-parameters of nonstationary time series was proposed by Tsatsannis and Giannkis (1993). The basic idea is to directly decompose the time-dependent autoregressive parameters into their wavelet representation and to select suitable wavelet coefficients for reconstruction. In either case, Kitagawa's (1983) "instantaneous spectrum" is calculated to obtain the actual spectral estimates. Applied to empirical data, both approaches lead to similar spectral estimates. However, simulations show how crucial the selection of wavelet coefficients is when applying the latter technique.