When we apply parametric models to the movement of stock prices, we don`t know whether they are really correct specifications. In the paper, any prior conditional mean structure is not assumed. By applying the nonparametric model, we see if it better performs (than the random walk model) in terms of out-of-sample prediction. An interesting finding is that the random walk model is still the best. There doesn`t seem to exist any form of nonlinearity (not to mention linearity) in stock prices that can be exploitable in terms of point prediction.