This paper presents new trading models for the stock market and test whether they are able to consistently generate excess returns from the Singapore Exchange (SGX). Instead of conventional ways of modeling stock prices, we construct models which relate the market indicators to a trading decision directly. Furthermore, unlike a reversal trading system or a binary system of buy and sell, we allow three modes of trades, namely, buy, sell or stand by, and the stand-by case is important as it caters to the market conditions where a model does not produce a strong signal of buy or sell. Linear trading models are firstly developed with the scoring technique which weights higher on successful indicators, as well as with the Least Squares technique which tries to match the past perfect trades with its weights. The linear models are then made adaptive by using the forgetting factor to address market changes. Because stock markets could be highly nonlinear sometimes, the Random Forest is adopted as a nonlinear trading model, and improved with Gradient Boosting to form a new technique—Gradient Boosted Random Forest. All the models are trained and evaluated on nine stocks and one index, and statistical tests such as randomness, linear and nonlinear correlations are conducted on the data to check the statistical significance of the inputs and their relation with the output before a model is trained. Our empirical results show that the proposed trading methods are able to generate excess returns compared with the buy-and-hold strategy.