Nonlinearity in Economics and Finance

这个项目的目标是整合混沌理论和非线性动力学的方法，现在用于自然和物理科学与计量经济学。该项目以一种为宏观经济学和金融学开发有用的新工具的方式做到了这一点。构建工具的策略是保持接近实际数据、实际计量实践和应用程序的现实——在过程中放弃抽象的一般性。具体项目包括：(1)将确定性混沌的残差诊断转化为确定性混沌的“残差检验”。(2)建立维数、Kolmogorov熵和Lyapunov指数的统计分布理论。将Brock提出的独立零假设检验的大小和功率特性与其他检验（如特征函数检验、分布函数检验和Cramer/ Von Mises形式的检验）进行比较和对比。(4)建立非线性的一般测试，并将其大小和功率特性与其他非线性测试（如双谱偏度测试、双线性测试、ARCH和GARCH测试以及非线性的半非参数测试）进行比较。(5)将这些测试应用于宏观经济学和金融学的数据。(6)建立宏观经济模型和均衡资产定价模型，解释所发现的非线性模式。

The objective of this project is to integrate methods of chaos theory and nonlinear dynamics now used in the natural and physical sciences with econometrics. The project does this in a way that develops useful new tools for macroeconomics and finance. The strategy for building tools is to stay close to the realities of actual data, actual econometric practice, and the applications-- giving up abstract generality in the process. The specific projects consist of the following: (1) turn the residual diagnostic for deterministic chaos into a "residual test" for deterministic chaos. (2) Work out statistical distribution theory for dimension, Kolmogorov entropy, and Lyapunov exponents. Compare and contrast the size and power characteristics of a test developed by Brock of the null hypothesis of independence with other tests such as characteristic function tests, distribution function tests, and Cramer/ Von Mises forms of the tests. (4) Build a general test for nonlinearity and compare its size and power characteristics to other nonlinearity tests such as the bispectral skewness test, tests for bilinearity, tests for ARCH and GARCH, and semi- nonparametric tests for nonlinearity. (5) Apply these tests to data in macroeconomics and finance. (6) Build macro economic models and equilibrium asset pricing models that explain the pattern of nonlinearity found.