Nonlinearity and Nonergodicity in Finance and Economics: Theory and Evidence

这项拨款继续支持美国国家科学基金会的一个项目，该项目将混沌理论和非线性动力学方法整合到自然科学和物理科学中，并与计量经济学相结合。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、实际计量实践和特定经济应用的现实——在过程中放弃抽象的一般性。这项拨款的主要部分是继续发展确定异质代理资产定价模型结构的方法。该方法将用于测试心理噪音交易与金融市场中基于信息的行为的相对重要性。更具体地说，该项目发现了足够的条件，使得弱依赖过程的“横截面”遍历定理和/或中心极限定理的组合，加上“聪明的钱”交易者玩噪音交易者，不会在均衡中消除噪音交易者的影响。这一研究路线的目的是发展一个严格的理论解释在金融市场的突变，如股市崩盘。为了对这一理论进行实证检验，GARCH/EGARCH类估计器进行了修改，以提高与交易利润测试（包括基本面和技术策略）衡量的财务数据的一致性。信息集扩大到包括交易量、股息/收益、利率、心理和社会学变量。该项目还完成了以前在国家科学基金资助下开始的工作，即开发非线性的一般测试，并将这些测试的尺寸和功率特性与其他非线性测试进行比较。特别注意力矩条件要求和混沌测试的目标，其中尺寸等于功率。

This grant continues NSF support of a project 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 specific economic applications-- giving up abstract generality in the process. The major part of this grant is concerned with continuing the development of a methodology for determining the structure of heterogeneous agent asset pricing models. This methodology would be used to test for the relative significance of psychological noise trading versus information-based behavior in financial markets. More specifically, the project finds sufficient conditions so that a combination of the "cross-sectional" ergodic theorem and/or the central limit theorem for weakly dependent processes coupled with "smart money" traders playing the noise traders does not wipe out the effect of noise traders in equilibrium. The purpose of this line of research is to develop a rigorous theoretical explanation of abrupt changes in financial markets such as stock market crashes. In order to empirically test this theory, the GARCH/EGARCH class of estimators are modified in order to improve consistency with financial data as measured by trading profits tests including both fundamental and technical strategies. The information set is enlarged to include volume, dividend/earnings, interest rates, psychological and sociological variables. The project also completes work begun under the previous NSF grant on the development of general tests for nonlinearity and the comparison of the size and power characteristics of these tests with other nonlinearity tests. Special attention is paid to moment condition requirements and the goal of a test for chaos where size equals power.