Financial time series and neural networks in a minority game context (original) (raw)
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I would also like to thank my colleagues at IPSOL Capital, where I completed a 4 month internship through the Mitacs program, in collaboration with the University. The financial support and insights into the world of financial modeling were very useful for my report. Particular thanks to Luc Gosselin whose insights into the world of finance were invaluable in the presentation of my results. Finally, I would like to thank my friend and colleague, Jean Hounkpe, who also provided me with valuable insights into mathematical modelling and never hesitated to lend me a helping hand in formulating my thoughts during the writing of this thesis.
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The Minority Game (MG) is a simple model for understanding collective behavior of agents in an idealized situation for a finite resource. It has been regarded as an interesting complex dynamical disordered system from a statistical mechanics point of view. In previous work, we have investigated the problem of learning the agent behaviors in the minority game by assuming the existence of one "intelligent agent" who can learn from other agent behaviors. In this paper, we propose a framework, Minority Game Data Mining (MGDM), that assumes the collective data are generated from combining the behaviors of variant groups of agents following the minority game. We then apply this framework to real-world time-series data analysis by testing on a few stocks from the Chinese market and the US Dollar-RMB exchange rate. The experimental results suggest that the winning rate of the new model is statistically better than a random walk.
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Cycles, determinism and persistence in agent-based games and financial time-series
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The Minority Game (MG), the Majority Game (MAJG) and the Dollar Game ($G) are important and closely-related versions of market-entry games designed to model different features of real-world financial markets. In a variant of these games, agents measure the performance of their available strategies over a fixed-length rolling window of prior timesteps. These are the so-called Time Horizon MG/MAJG/$G (THMG, THMAJG, TH$G)s. Their probabilistic dynamics may be completely characterized in Markov-chain formulation. Games of both the standard and TH variants generate time-series that may be understood as arising from a stochastically perturbed determinism because a coin toss is used to break ties. The average over the binomially-distributed coin-tosses yields the underlying determinism. In order to quantify the degree of this determinism and of higher-order perturbations, we decompose the sign of the time-series they generate (analogous to a market price time series) into a superposition of weighted Hamiltonian cycles on graphs-exactly in the TH variants and approximately in the standard versions. The cycle decomposition also provides a "dissection" of the internal dynamics of the games and a quantitative measure of the degree of determinism. We discuss how the outperformance of strategies relative to agents in the THMG-the "illusion of control"and the reverse in the THMAJG and TH$G, i.e., genuine control-may be understood on a cycle-by-cycle basis. The decomposition offers as well a new metric for comparing different game dynamics to real-world financial time-series and a method for generating predictors. We apply the cycle predictor a real-world market, with significantly positive returns for the latter.
Cycles, determinism and persistence in agent-based games and financial time-series: part II
Quantitative Finance, 2012
The Minority Game (MG), the Majority Game (MAJG) and the Dollar Game ($G) are important and closely-related versions of market-entry games designed to model different features of real-world financial markets. In a variant of these games, agents measure the performance of their available strategies over a fixed-length rolling window of prior timesteps. These are the so-called Time Horizon MG/MAJG/$G (THMG, THMAJG, TH$G)s. Their probabilistic dynamics may be completely characterized in Markov-chain formulation. Games of both the standard and TH variants generate time-series that may be understood as arising from a stochastically perturbed determinism because a coin toss is used to break ties. The average over the binomially-distributed coin-tosses yields the underlying determinism. In order to quantify the degree of this determinism and of higher-order perturbations, we decompose the sign of the time-series they generate (analogous to a market price time series) into a superposition of weighted Hamiltonian cycles on graphs-exactly in the TH variants and approximately in the standard versions. The cycle decomposition also provides a "dissection" of the internal dynamics of the games and a quantitative measure of the degree of determinism. We discuss how the outperformance of strategies relative to agents in the THMG-the "illusion of control"and the reverse in the THMAJG and TH$G, i.e., genuine control-may be understood on a cycle-by-cycle basis. The decomposition offers as well a new metric for comparing different game dynamics to real-world financial time-series and a method for generating predictors. We apply the cycle predictor a real-world market, with significantly positive returns for the latter.
Some Remarks About Financial Market Modelling Using a Minority Game Approach
The methods adopted by static physics corroborating the existence of electromagnetic forces are applicable to the theory of financial markets. Perceived from a classically physical angle, the financial market is defined as a system composed of several individual entries cooperating upon electromagnetic principles. The approach concerned gives rise to a certain model of financial market, otherwise known as a minority game. In the case of minority game, the allocation of securities and funds is conditioned exclusively upon the fluctuation of prices, where a higher tendency to purchase goods and stocks results in the scale being more profitable and vice versa. Thus players from a minority group gain a prevailing position.