Nonlinearity and Nonergodicity in Finance and Economics: Theory and Evidence

这笔赠款继续支持NSF将目前在自然科学和物理科学中使用的混沌理论和非线性动力学方法与计量经济学相结合的项目。该项目以一种为宏观经济和金融开发有用的新工具的方式做到了这一点。构建工具的策略是紧贴实际数据、实际计量经济学实践和具体经济应用的现实--放弃过程中抽象的概括性。这笔赠款的主要部分是继续开发确定不同代理资产定价模型结构的方法。这一方法将被用来测试心理噪音交易与金融市场基于信息的行为的相对重要性。更具体地说，该项目找到了充分条件，使得弱相依过程的“横截面”遍历定理和/或中心极限定理与扮演噪声交易者的“聪明的钱”交易者相结合，不会消除均衡中的噪声交易者的影响。这条研究路线的目的是为金融市场的突变(如股市崩盘)发展一个严谨的理论解释。为了对这一理论进行实证检验，对GARCH/EGARCH类估计量进行了修正，以提高与通过包括基本策略和技术策略在内的交易利润检验所衡量的金融数据的一致性。信息集被扩大到包括交易量、股息/收益、利率、心理和社会学变量。该项目还完成了在之前的NSF拨款下开始的开发一般非线性测试以及将这些测试的大小和功率特性与其他非线性测试进行比较的工作。特别注意的是矩条件的要求，以及在大小等于功率的情况下测试混沌的目标。

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.