Goodness of fit test for the multifractal model of asset returns

This paper explores extensions to the random walk model for time series in finance. There is some disagreement about the suitability of multifractal probability models, but they have compelling attributes. Research that has found no evidence to support the multifractal model has used testing procedures that do not have known statistical power. Therefore, there is an opportunity for new methodology. This paper presents a testing procedure to determine if data follows a multifractal or monofractal process. Using simulation, the paper derives the power of the test. Although the power is low, the test suggests that some observed prices do follow multifractal behaviour. This is a strong result. Further, this work suggests there will be further disagreement in the literature going forward due to the difficulty of identifying multifractal data.