论文标题
非线性动力学及其在财务时间序列中的应用几何分析
A geometric analysis of nonlinear dynamics and its application to financial time series
论文作者
论文摘要
讨论了一种分析非线性振荡的几何方法。我们考虑通过二阶普通微分方程建模的非线性振荡，而无需指定函数形式。通过将微分方程转换为一阶普通微分方程的系统，将轨迹嵌入$ r^3 $作为曲线中，从而将原始状态的时间演变转换为曲线的行为$ r^3 $，或沿曲线的向量场。我们分析了矢量场，以研究非线性振荡的动态特性。尽管未指定模型的函数形式，但可以通过非参数滤波方法来估计矢量场和相关数量。我们将拟议的分析应用于日本股票价格指数的时间序列。该应用程序表明，向量字段及其导数将用作拾取各种信号的工具，以帮助理解股票价格指数的动态属性。
A geometric method to analyze nonlinear oscillations is discussed. We consider a nonlinear oscillation modeled by a second order ordinary differential equation without specifying the function form. By transforming the differential equation into the system of first order ordinary differential equations, the trajectory is embedded in $R^3$ as a curve, and thereby the time evolution of the original state can be translated into the behavior of the curve in $R^3$, or the vector field along the curve. We analyze the vector field to investigate the dynamic properties of a nonlinear oscillation. While the function form of the model is unspecified, the vector fields and those associated quantities can be estimated by a nonparametric filtering method. We apply the proposed analysis to the time series of the Japanese stock price index. The application shows that the vector field and its derivative will be used as the tools of picking up various signals that help understanding of the dynamic properties of the stock price index.
