On the weak convergence of sequences of circuit processes: a probabilistic approach

Kalpazidou, S.

doi:10.2307/3214574

Cited by 5 publications

(1 citation statement)

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“…We see that this has happened here. Formally, the convergence of to is in general weak and "almost sure" [16]. We will see by comparison to numerical simulation that the small error thus introduced has no effect on our use of the ].…”

Section: Analytic Form Of a Cycle Decompositionmentioning

confidence: 97%

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

Satinover

Sornette

2012

Quantitative Finance

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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. m m c c i ij j i J J J c i j J =1 if (i,j) is a directed edge of , 0 otherwise. In addition, c J c i c c J

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Section: Analytic Form Of a Cycle Decompositionmentioning

confidence: 97%