英文标题：
《Fractality of profit landscapes and validation of time series models for
  stock prices》
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作者：
Il Gu Yi, Gabjin Oh, and Beom Jun Kim
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最新提交年份：
2013
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英文摘要：
  We apply a simple trading strategy for various time series of real and artificial stock prices to understand the origin of fractality observed in the resulting profit landscapes. The strategy contains only two parameters $p$ and $q$, and the sell (buy) decision is made when the log return is larger (smaller) than $p$ ($-q$). We discretize the unit square $(p, q) \\in [0, 1] \\times [0, 1]$ into the $N \\times N$ square grid and the profit $\\Pi (p, q)$ is calculated at the center of each cell. We confirm the previous finding that local maxima in profit landscapes are scattered in a fractal-like fashion: The number M of local maxima follows the power-law form $M \\sim N^{a}$, but the scaling exponent $a$ is found to differ for different time series. From comparisons of real and artificial stock prices, we find that the fat-tailed return distribution is closely related to the exponent $a \\approx 1.6$ observed for real stock markets. We suggest that the fractality of profit landscape characterized by $a \\approx 1.6$ can be a useful measure to validate time series model for stock prices.
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中文摘要：
我们对真实和人工股价的各种时间序列应用一种简单的交易策略，以了解由此产生的利润景观中观察到的分形的起源。该策略只包含两个参数$p$和$q$，当日志返回大于（小于）$p$（$-q$）时，就会做出卖出（买入）决策。我们将[0，1]\\乘以[0，1]$中的单位平方$（p，q）离散化为$N \\乘以N$平方网格，并在每个单元的中心计算利润$\\Pi（p，q）$。我们证实了之前的发现，即利润景观中的局部极大值是以分形的方式分散的：局部极大值的数量M遵循幂律形式$M\\sim N^{a}$，但标度指数$a$在不同的时间序列中是不同的。通过对真实股票价格和人工股票价格的比较，我们发现厚尾收益率分布与真实股票市场观察到的指数$a\\约1.6$密切相关。我们认为，以$a \\约1.6美元为特征的利润格局的分形性可以作为一个有用的衡量标准，来验证股票价格的时间序列模型。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Statistical Finance        统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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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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