The main goal of this dissertation is to compare the performance of linear and nonlinear models to forecast 23 assets of the American Stocks Market. The Heteroscedastic STAR-Tree Model is proposed using the STAR- Tree (Smooth Transition AutoRegression Tree) methodology applied to heteroscedastic time series. As assets returns and realized volatility intraday data are available, the returns series are transformed by dividing each return by its realized volatility, which gives homocedastic series. The model is a combination of the STAR (Smooth Transition AutoRegression) methodology and the CART (Classification and Regression Tree) algorithm. The resulting model can be interpreted as a smooth transition multiple regime regression. The model specification is done by Lagrange Multiplier tests that indicate the node to be split and the corresponding transition variable. The comparison models used are the Mean model, Naive method, ARX linear models and Neural Networks. The forecasting models were evaluated through statistical and financial measures. The financial results are based on an automatic trading rule that signals buy and hold moments in each stock. The Heteroscedastic STAR-Tree Model statistical performance was equivalent to the other models, however its financial performance was superior for most of the series. The STAR-Tree methodology was also applied for forecasting the realized volatility, and the forecasts were used in financial leverage analysis.