In classic financial theory, financial markets are thought to be efficient. Therefore, stocks are assured to have any information already about them already used in the price discovery process which means models cannot forecast the future price of stocks. Empirical test of this hypothesis frequently use linear models to assess whether the hypothesis is true. However, there is no reason to believe that stock prices are linearly related to the past prices or other information like volume. In this thesis, we conduct an empirical test of market efficiency using models which do not necessarily assume that the price is linearly related to past prices. Specifically, our goal is to classify a future stock price as either a positive return or a negative return. We find that even after allowing for a nonlinear structure, the returns are indeed still unforecastable and the efficient market hypothesis holds.