## STATISICAL AND MULTIFRACTAL PROPERTIES OF TIME SERIES GENERATED BY A MODIFIED MINORITY GAME

### BibTeX

@MISC{Kuperin_statisicaland,

author = {Yu. A Kuperin and M. M. Morozova},

title = {STATISICAL AND MULTIFRACTAL PROPERTIES OF TIME SERIES GENERATED BY A MODIFIED MINORITY GAME},

year = {}

}

### OpenURL

### Abstract

In this paper it was developed a modification of the known multiagent model Minority Game, designed to simulate the behavior of traders in financial markets and the resulting price dynamics on the abstract resource. The model was implemented in the form of software. The modified version of Minority Game was investigated with the aim of reproducing the basic properties of real financial time series. It was proved that such properties as the clustering of volatility, the Levy distribution and multifractality are inherent for generated by this version of the Minority Game time series of prices. PACS 89.65.Gh 1.

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Citation Context ...ts can be calculated. For the readers convenience we give below the basic information from the multifractal analysis. 2.1. Fractal dimension In the definition of fractals, the main idea by Mandelbrot =-=[13]-=- has been related with the notion of selfsemilarity. In other words fractals are scale invariant objects. This scale invariance may be exact or statistical. It can be shown [13] that for fractals obje... |

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Citation Context ...prices for an abstract resource, which should have the most important features of real financial time series, namely: multifractality, heavy-tailed probability distributions and volatility clustering =-=[17, 21, 30]-=-. For achieving the above stated objectives there have been addressed several subtasks. First, we have developed a minimal list of modifications of the Minority Game, which was enough to ensure that t... |

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Citation Context ... ⎤ ln F( q) = i ⋅δ ⋅ q − c ⋅ q ⋅ ⎢1 − i ⋅ β ⋅ ⋅ tg ⎥, α ≠ 1 ⎣ q 2 ⎦ ⎡ q ⎤ ln F( q) = i ⋅δ ⋅ q − c ⋅ q ⋅ ⎢1 − i ⋅ β ⋅ ⋅ ln q ⎥, α = 1 ⎣ q ⎦ Distribution of Levy is characterized by four parameters: α ∈=-=[0,2]-=- β ∈− [ 1,1] с∈R + δ ∈ R Hereα is a certain parameter often called characteristic exponent, β is the skewness parameter, c is the scale parameter and δ is the location parameter. Characteristic expone... |

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Citation Context ...ods have been also implemented in the form of software. Attempts to modify the original version of the Minority Game in order to obtain multifractal time series have been made before. For example, in =-=[12]-=- the authors have attempted to develop a modification of the Minority Game, which serve to demonstrate the multifractal properties. To achieve this effect, the author had to make not a realistic step:... |

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Citation Context ...e dependence variance. Stability can be observed only on the little time scale, in the other cases convergence to normal distributions is observed. To overcome this problem P. Mantegna and H. Stanley =-=[23, 24, 25]-=- proposed truncated Levy distribution for real date. In case of truncated Levy distribution central part is described by stableLevy and tails have exponential drop-down. Such modification provides Ga... |

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Citation Context ...uch as linguistics, medicine, informatics etc, where the multifractal analysis is also very successful. In particular, it can be used in data mining of financial data. The numerous studies (see, e.g. =-=[10, 11, 12]-=-) have shown that financial time series possess the mulifractal properties and hence the Holder exponents can be calculated. For the readers convenience we give below the basic information from the mu... |

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Citation Context ...time series { } N i i . Suppose that for the time series { } ' N X i i= 1 the Holder exponent is equal to α . Knowing α , let us calculate (α ) C for the set { } ' N X i i= 1 by means of the equation =-=(3)-=-. Further for the set N { Xi} ' the quantities C( β k ) are calculated. i= N + 1 But the procedure of calculations will be changed. In step by step calculating the numbers C( β k ) let us stop at that... |

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Citation Context ...ed by this version of the Minority Game time series of prices. PACS 89.65.Gh 1. INTRODUCTION The main objective of this work was to develop modifications of the known multi-agent models Minority Game =-=[9, 10, 23]-=-, which is designed to simulate the behavior of traders in the financial market subject to the conditions most close to reality. Based on the dynamics of traders such game should generate a time serie... |

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Citation Context ...ed by this version of the Minority Game time series of prices. PACS 89.65.Gh 1. INTRODUCTION The main objective of this work was to develop modifications of the known multi-agent models Minority Game =-=[9, 10, 23]-=-, which is designed to simulate the behavior of traders in the financial market subject to the conditions most close to reality. Based on the dynamics of traders such game should generate a time serie... |

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