Analysis of financial time series through forbidden patterns

Abstract

The forbidden pattern is consistently considered to be an instrument of discriminating the potentially deterministic time series from random one. As a complexity parameter, the forbidden pattern is valuable for the real-world time series since noise eliminations are not needed—it focuses on the comparison of adjacent values. In some cases, based on the permutation entropy and the Bandt–Pompe (BP) methodology, it turns to analogous results with the Lyapunov exponent, with faster calculation and better robustness, however. In this work, we use the approach of the number of forbidden patterns to distinguish completely random behavior and potentially deterministic dynamic system in the real world. In particular, we pay attention to the performance of the method in the financial time series. In addition, we are concerned about the effect of time delays on determinism of stock indices and make a discussion of the sensitivity of different stock indices to time delays. Moreover, in this paper we focus on the evolution of deterministic behavior, pointing out that it is effective to use this method to quantify the degree of determinism in different time states. We can see that the approach of the number of forbidden patterns has excellent characteristics in terms of capturing potential properties of financial systems.