Modelling Stock Market Excess Returns by Markov Modulated Gaussian Noise

A basic analysis of stock market excess return data shows both linear and non-linear dependence present. Previous papers have used this to argue that it must therefore be possible to predict future values. However, this paper shows that the linear and non-linear dependence can be explained by simply allowing the mean and variance of Gaussian noise to be modulated by a (typically 3 state) hidden Markov model. Attempting to fit a Markov modulated AR process proved fruitless; the conclusion is that there is no AR-predictability present in excess return data.