Gaussian mixture modelling to detect random walks in capital markets

In this paper, Gaussian mixture modelling is used to detect random walks in capital markets with the Kolmogorov-Smirnov test. The main idea is to use Gaussian mixture modelling to fit asset return distributions and then use the Kolmogorov-Smirnov test to determine the number of components. Several quantities are used to characterize Gaussian mixture models and ascertain whether random walks exist in capital markets. Empirical studies on China securities markets and Forex markets are used to demonstrate the proposed procedure.