Cycles, determinism and persistence in agent-based games and financial time-series: part II

The present article constitutes part II of a series of two reports in which we study the decomposition of synthetic and real financial time-series into a superposition of weighted Hamiltonian cycles on graphs. Part II further analyses the cycle-decomposition method introduced in part I for the Minority Game (MG), the Majority Game (MAJG) and the Dollar Game ($G), in order to gain insight into the ‘illusion of control’ that certain of these games demonstrate, i.e. the fact that the strategies outperform the agents that deploy them. We also illustrate both numerical and analytical methods for extracting cycles from a given time-series and apply the method to a number of different real-world data sets, in conjunction with an analysis of persistence.