Estimation and Prediction of Generalized Growth Curve with Grouping Variances in AR( q ) Dependence Structure

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 Σ = D σ CD σ where C is the correlation matrix with stationary autoregression process of order q , q < p and D σ is a diagonal matrix with p elements divided into g (≤ p ) groups, i.e., D σ is a function of {σ 1 , …, σ g } and – 1 < ρ < 1 and σ l , l = 1, …, g , are unknown. We consider both parameter estimation and prediction of future values. Results are illustrated with real and simulated data.