在自相關且異質變異數的共變異結構之成長曲線估計與預測

Abstract

本論文探討成長曲線在自相關且異質變異數之共變異矩陣結構，我們將共變異矩陣結構延伸到一般的自相關而且隨機效應之結構下，我們也探討異質變異數且一般自相關的共變異矩陣結構。至於異質變異數，我們用群組的方式來分類或者直接用GARCH模式來建構。我們給這些共變異矩陣結構下的成長曲線模型的參數估計以及預測，最後用真實的資料以及模擬的資料來說明這些結構下的一些結果。

We consider the generalized growth curve model when the covariance matrix has autoregressive dependence structure with non-homogeneity of variances. We consider an extension of the covariance structure to an AR(q) process with random effects and consider that the covariance matrix is DCD where C is the correlation matrix and D is a diagonal matrix with p unknown elements. In other wards, we will consider growth curve model with random effects or with grouping of variances or with GARCH model in AR(q) or general autoregressive dependence structure. We give both parameter estimation and prediction of future values. Results are illustrated with real and simulated data.