Nonlinear Dynamics, Chaos, and Instability

Chaos theory has touched on such fields as biology, cognitive science, and physics. By providing a unified and complete explanation of new statistical methods that are useful for testing for chaos in data sets, Brock, Hsieh, and LeBaron show how the principles of chaos theory can be applied to such areas of economics and finance as the changing structure of stock returns and nonlinearity in foreign exchange. They use computer models extensively to illustrate their ideas and explain this frontier research at a level of rigor sufficient for others to build upon as well as to verify the soundness of their arguments.The authors, who have played a major role in developing basic testing methods that are effective in detecting chaos and other nonlinearities, provide a detailed exposition of empirical techniques for identifying evidence of chaos.

They introduce and describe the BDS statistic, an easy-to-use test that detects the existence of potentially forecastable structure, nonstationarity, or hidden patterns in time-series data and that can be adapted to test for the adequacy of fit of forecasting models. An extensive performance evaluation of the BDS is included.Nonlinear Dynamics, Chaos, and Instability also reviews important issues in the theoretical economics literature on chaos and complex dynamics, surveys existing work on the detection of chaos and nonlinear structure, and develops models and processes to discover predictable sequencing in time-series data, such as stock returns, that currently appear random. William A.

Brock is Vilas Research Professor of Economics and Blake LeBaron is Assistant Professor of Economics, both at the University of Wisconsin, Madison. David A. Hsieh is Professor of Business at the Fuqua School of Business, Duke University.