ABSTRACT
This chapter presents the procedures for reducing measurement noise in experimental time series data. It begins with an account of the singular value decomposition (SVD) method for noise reduction. Schreiber showed how the effect of SVD can be visualized. The linearization process prior to the extraction of principal components operates on points defined within a small ellipsoid. Time-series prediction methods can detect changes in the nonlinear dynamics of a single time series, as occurs in highly nonstationary time series such as EEG. Vibe and Vesin evaluated the local intrinsic dimension (LID) index, which provides an upper bound to the fractal dimension of an attractor. The LID index involves computing the number of degrees of freedom for a sample and then averaging this value across the attractor. The chapter concludes some illustrative applications of noise reduction and prediction methods for the analysis of experimental time series of interest to psychologists.
