Much of theoretical and empirical economics and finance is based on adaptations of linear differential and difference equations.  While fine up to a point, there is no compelling reason to think that linear equations are adequate.  Nonlinear dynamics offers an alternative to using linear equations to describe sequences.

Advances in the 1980s and 1990s indicated that nonlinear equations can generate much more complicated response patterns than can linear equations.  Chaos theory itself involves generating seemingly random outcomes from deterministic sequences.  Chaos theory is not particularly informative in economics or finance.

Nonlinear time series analysis, on the other hand, can be extremely informative about aspects of the economy and maybe especially about financial markets.  Nonlinear time series can have much more complicated responses of the economy to shocks. Nonlinear time series analysis also can provide a more detailed understanding of the underlying complexity in financial markets.

My work on nonlinear dynamics examines the importance of nonlinearities in the economy and financial markets. Nonlinear Time Series and Financial Applications is a very brief summary of nonlinear time series analysis based on two lectures at the University of Rome in Fall 2000.

“A little economics goes a long way and a lot of data doesn't hurt.” That's my conclusion from “Index Arbitrage and Nonlinear Dynamics between the Futures and Cash S&P 500” with Peter Locke and Wei Yu. 

We examine arbitrage between the S&P 500 index and S&P 500 futures and find that nonlinear time series analysis is quite helpful for understanding that arbitrage. You can get a copy of this paper which was published in the Review of Financial Studies at the RFS web site.

What are the implications of nonlinearities for the economy as measured by such aggregate variables such as the unemployment rate, industrial production and interest rates? Cora Barnhart and I examine this in Nonlinear Aspects of Business Fluctuations. We find that the there is a common nonlinearity in business cycles.

Threshold autoregressions, particularly simple nonlinear equations, are used in the papers above. These equations depend heavily on a time delay to trigger nonlinear responses. Richard Ashley and I examine the implications of using data at different frequencies to estimate such nonlinear models in Time Aggregation and Threshold Autoregressions. We find that there can be dire consequences from using data at longer time periods.

What happens if a government authority attempts to stabilize an economy with underlying nonlinearities? Dire consequences are possible although not inevitable as I show in "Stabilization Policy Can Lead to Chaos" published in Economic Inquiry 30 (January 1992), 40-46. This paper is available in many libraries.

The Society for Nonlinear Dynamics and Econometrics is for those with a special interest in the implications of nonlinear dynamics for economics and finance. I may be biased since I am the new President of the Society, but I do think that there is some interesting stuff at the site.

The Society for Nonlinear Dynamics and Econometrics has annual meetings, with the most recent ones held in Florence, Italy in March 2003 and Atlanta, Georgia in March 2004.  The March 2005 meeting is in London. The program and other information are available at the SNDE web site, as is information about a mailing list to which you can subscribe. You can keep informed about the society on the mailing list, which is discussed at the website.