Create Linear Models and the Hypothesis of Efficient Markets

Theory

The hypothesis of efficient markets tells us that financial markets are information efficient. Market prices of shares contain all available information about future gains, i.e. that means: The best estimate for tomorrows price is todays price plus some average return β0:
p^t+1=pt+β0.
The returns cannot be predicted, if historical returns rt−1,rt−2,… cannot be used to build a prediction model, i.e. the fitting regression model for the return is
rt=β0+ϵt.
The average return β0 can then be estimated with standard regression models. The return can be predicted, if historical returns rt−1,rt−2,… can be used to build a prediction model. In the most simple case use an AR(1) model (auto-regressive model of order 1).
rt=β0+β1rt−1+ϵt.

Conclusion: use statistical methods to determine, whether returns are predictable.