Analysis of Covariance Structures in Time Series

Jennifer S K Chan,S T Boris Choy

doi:10.6339/jds.2008.06(4).432

Abstract

Longitudinal data often arise in clinical trials when measure ments are taken from subjects repeatedly over time so that data from each subject are serially correlated. In this paper, we seek some covariance matri ces that make the regression parameter estimates robust to misspecification of the true dependency structure between observations. Moreover, we study how this choice of robust covariance matrices is affected by factors such as the length of the time series and the strength of the serial correlation. We perform simulation studies for data consisting of relatively short (N=3), medium (N=6) and long time series (N=14) respectively. Finally, we give suggestions on the choice of robust covariance matrices under different situ ations.

Highlights

In ordinary regression, the error terms are assumed to be independently and identically distributed with a constant variance
Instead of resorting to this complicated techniques, we propose the generalized regression models in which the covariance matrices are based on widely used forms, and we seek those structures that are robust to misspecification of the true structures which are often unknown in practice
In order to study the interaction effect of the length of the time series and the strength of the serial correlation on the choice of robust covariance structure, two more simulation studies have been done with level of ρ in AR1 set to 0.7 and 0.35 for the two data sets containing time series of N = 3 and N = 14 respectively

Summary

Introduction

The error terms are assumed to be independently and identically distributed with a constant variance. These assumptions are not always true in practice. When subjects are measured repeatedly over time in longitudinal studies, observations from each subject are usually serially correlated. Such time series are common in clinical trials and stock markets. T. Boris Choy modeled the covariance matrix in terms of its standard deviations and correlation matrix and estimated the parameters using a Bayesian approach. Instead of resorting to this complicated techniques, we propose the generalized regression models in which the covariance matrices are based on widely used forms, and we seek those structures that are robust to misspecification of the true structures which are often unknown in practice

Objectives

Results

Conclusion