Nonlinearity in Economics and Finance

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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.