Python Data Analysis Cookbook

Determining market efficiency with autoregressive models

According to the efficient-market hypothesis (refer to the Examining the market with the non-parametric runs test recipe), all information about an asset is immediately reflected in the price of the asset. This means that previous prices don't influence the current price. The following equations specify an autoregressive model (7. 13) and a restricted model (7. 14) with all the coefficients set to zero:

If we believe the market to be efficient, we would expect the unrestricted model to have nothing to add over the restricted model, and, therefore, the ratio (7. 15) of the respective R-squared ...