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趋势跟踪与逆向交易规则如何影响股票价格混沌

文章 arXiv papers · 作者: Li-Xin Wang
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总结

本文分析一个围绕移动平均线交易规则构建的股价动态模型。模型将价格混沌行为归因于趋势跟踪需求与逆向需求的相互作用，并描述了与发散、混沌和振荡相关的参数范围。据报告，该模型有无穷多个均衡点，且全部不稳定。分析还根据模型参数推导出李雅普诺夫指数，并研究即使价格处于混沌状态时收益波动率的表现。

作者报告称，波动率会迅速趋近一个常数，并使用蒙特卡洛模拟估计其与模型参数的关系，同时考察收益何时呈现独立性。绘制的奇异吸引子和收益分布展示了复杂行为和肥尾。这些发现针对特定数学模型；描述没有提供市场数据实证验证，也不能证明该模型的动态能够解释实际股票收益。结论取决于模型假设和参数选择。

核心观点

  • 模型将价格混沌与趋势跟踪和逆向交易规则的相互作用联系起来。
  • 模型中的均衡点均被描述为不稳定，参数范围决定发散、混沌和振荡。
  • 分析推导出李雅普诺夫指数，并将其与短期波动行为联系起来。
  • 研究使用蒙特卡洛模拟估计模型收敛后的波动率。
  • 文中描述的混沌动态是模型结果，文本未说明实证验证。

标签

股票趋势跟踪均值回归波动率统计学
全文
# Dynamical Models of Stock Prices Based on Technical Trading Rules Part II: Analysis of the Models


# Dynamical Models of Stock Prices Based on Technical Trading Rules Part II: Analysis of the Models









In Part II of this paper, we concentrate our analysis on the price dynamical model with the moving average rules developed in Part I of this paper. By decomposing the excessive demand function, we reveal that it is the interplay between trend-following and contrarian actions that generates the price chaos, and give parameter ranges for the price series to change from divergence to chaos and to oscillation. We prove that the price dynamical model has an infinite number of equilibrium points but all these equilibrium points are unstable. We demonstrate the short-term predictability of the return volatility and derive the detailed formula of the Lyapunov exponent as function of the model parameters. We show that although the price is chaotic, the volatility converges to some constant very quickly at the rate of the Lyapunov exponent. We extract the formula relating the converged volatility to the model parameters based on Monte-Carlo simulations. We explore the circumstances under which the returns show independency and illustrate in details how the independency index changes with the model parameters. Finally, we plot the strange attractor and return distribution of the chaotic price model to illustrate the complex structure and fat-tailed distribution of the returns.

在遵守原作品许可的前提下，附作者信息全文展示。 许可协议: abstract CC0

此摘要由 Stratmill 研究智能体根据原文撰写，并非原文副本。