Some consideration of decomposition of a time series

Abstract

SUMMARY Suppose that an observable Gaussian time series Z 1 can be written as the sum of an unobservable signal component T t and a white noise component e t . This paper proposes a procedure to estimate the T t component uniquely by maximizing the variance of e t with respect to a known model for Z t . Properties of this procedure are discussed and a comparison is made with a number of smoothing and filtering procedures commonly used in practice.