Sequential least-squares prediction based on spectral analysis

Abstract

A spectral representation for time series analysis is formulated on the basis of classical least-squares theory, and is extended for application to the prediction of a random sequence with a sequential updating of model coefficients based on pre-computed eigenvector components and current online data. The solution for updating the time series coefficients is shown to be directly analogous to the form of piecewise solution of the steady-state electrical network problem based on Kron's method of tearing and interconnection. The sensitivity of the spectral prediction algorithm based on the eigenvalue properties of the defining covariance data matrix is also developed.