This thesis is essentially devoted to models for analysis and forecasting of vector time series, where the seasonal behavior is the main focus, and a Bayesian procedure of sequential estimation is adopted. The basic structure of the non-linear multivariate model, of seasonal growth multiplicative for time series, consists of a locally linear trend component for each individual series and a shared multiplicative seasonal component common to all marginal series. The procedure of sequential estimation is based on analytic transformations to obtain a conjugate analysis, representing a non-linear extension of the algorithm by Barbosa and Harrison (1992) for multivariate dynamic linear models. Details of the proposed procedure and of the implementation are shown, as well examples of the application of the method, with simulated and real data. For real data, the brazilian electricity demand values were chose. The forecasting methodology adopted by the energy companies is also present in this work.