Nonlinearity and Nonergodicity in Finance and Economics: Theory and Evidence

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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.