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摘要翻译：
对金融时间序列更真实建模的探索揭示了真实市场的几个程式化事实。在这项工作中，我们着重研究价格和指数信号中的多重分形性质。虽然通常的少数博弈(MG)模型不表现多重分形性，但我们在这里研究它的一个变体。我们证明了非遍历阶段的非同步MG模型是多重分形的，在这个意义上，与其他程式化事实一起，构成了一个更好的建模工具。利用结构函数(SF)方法检测MG模型产生的时间序列的平稳性和标度范围，并从SF的线性（非线性）行为中识别出分形（多重分形）状态。最后，利用小波变换模极大值(WTMM)技术，得到了其在不同动力学状态下的多重分形谱宽度。
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英文标题：
《Multifractal regime transition in a modified minority game model》
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作者：
Antonio F. Crepaldi, Camilo Rodrigues Neto, Fernando F. Ferreira and
Gerson Francisco
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最新提交年份：
2007
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Trading and Market Microstructure 交易与市场微观结构
分类描述：Market microstructure, liquidity, exchange and auction design, automated trading, agent-based modeling and market-making
市场微观结构，流动性，交易和拍卖设计，自动化交易，基于代理的建模和做市
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一级分类：Physics 物理学
二级分类：Physics and Society 物理学与社会
分类描述：Structure, dynamics and collective behavior of societies and groups (human or otherwise). Quantitative analysis of social networks and other complex networks. Physics and engineering of infrastructure and systems of broad societal impact (e.g., energy grids, transportation networks).
社会和团体（人类或其他）的结构、动态和集体行为。社会网络和其他复杂网络的定量分析。具有广泛社会影响的基础设施和系统（如能源网、运输网络）的物理和工程。
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英文摘要：
The search for more realistic modeling of financial time series reveals several stylized facts of real markets. In this work we focus on the multifractal properties found in price and index signals. Although the usual Minority Game (MG) models do not exhibit multifractality, we study here one of its variants that does. We show that the nonsynchronous MG models in the nonergodic phase is multifractal and in this sense, together with other stylized facts, constitute a better modeling tool. Using the Structure Function (SF) approach we detected the stationary and the scaling range of the time series generated by the MG model and, from the linear (nonlinear) behavior of the SF we identified the fractal (multifractal) regimes. Finally, using the Wavelet Transform Modulus Maxima (WTMM) technique we obtained its multifractal spectrum width for different dynamical regimes.
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PDF链接：
https://arxiv.org/pdf/0709.0976
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