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We propose parametric and nonparametric data-driven approaches to model covariance structures for longitudinal data.Based on a modified Cholesky decomposition, the within-subject covariance matrix is decomposed into a unit lower triangular matrix involving generalized autoregressive coecients and a diagonal matrix involving inmvation variances.Generalized estimation equations estimation is proposed to obtain the parameters of the mean, generalized autoregressive coecients and log-innovation variances, simultaneously.Local polynomial smoothing estimation is proposed to model the nonparametric smoothing functions.Real data sets are analyzed for illustration.Simulation studies are made to evaluate the ecacy of the proposed method and compare to the related literature work.This is joint work with Prof.Pan, J.Dr.Huang, C.and Prof.Li, R..