Application of Kolmogorov complexity and universal codes to identity   testing and nonparametric testing of serial independence for time series
  We show that Kolmogorov complexity and such its estimators as universal codes (or data compression methods) can be applied for hypotheses testing in a framework of classical mathematical statistics. The methods for identity testing and nonparametric testing of serial independence for time series are suggested. 
Boris Ryabko and Jaakko Astola and Alex Gammerman