Estimation and prediction of generalized growth curve with grouping variances in AR(q) dependence structure

Abstract

In this paper we consider maximum likelihood analysis of generalized growth curve model with the Box-Cox transformation when the covariance matrix has AR(q) dependence structure with grouping variances. The covariance matrix under consideration is Sigma = DsigmaCDsigma where C is the correlation matrix with stationary autoregression process of order q, q < p and D-&sigma; is a diagonal matrix with p elements divided into g(&LE; p) groups, i.e., D-&sigma; is a function of {&sigma;(1),..., &sigma;(g)} and -1 < p < 1 and &sigma;(l), l = 1,...g, are unknown. We consider both parameter estimation and prediction of future values. Results are illustrated with real and simulated data.