Python Data Analysis Cookbook

Testing for random walks

The random walk hypothesis (RWH) just like the efficient-market hypothesis (refer to the Examining the market with the non-parametric runs test recipe) claims that the market cannot be beaten. The RWH stipulates that asset prices perform a random walk. You can in fact generate pretty convincing stock price charts just by flipping a coin repeatedly.

In 1988, finance professors Lo and MacKinlay constructed a test for the RWH using the natural log(arithm) of asset prices as data. The test specifies the log prices to drift around a mean (7.9). We expect price changes for different frequencies (for instance, one-day and two-day periods) to be random. Furthermore, the variances (7.10 and 7.11) at two different frequencies are ...