Applied Regression and Analysis of Variance for Stationary Time Series

Abstract

In the area of applied time series analysis a commonly occurring problem involves the detection and estimation of signals (regression functions) imbedded within a collection of independent identically distributed noise processes. A general linear model which represents each observed time series as the sum of a wide sense stationary error process and a vector of regression functions operated on by a matrix of time invariant observables includes as special cases many signal models of interest. In this article a possible unified approach to estimation and tests of hypotheses for this linear model is presented. Asymptotic regression estimates and analysis of variance (power) tables are presented in the frequency domain and simple derivations for the probability distributions of the sums of squares are given. The resulting analysis of power partitions the spectral power in each frequency band into components which can be attributed directly to each of the regression functions. As an example, a sample of ten time series is analyzed which contains a mean value function and an effect function in the presence of error.