CHAOS IN ECONOMICS AND FINANCE

Abstract

In this talk, we explain the history and the use of chaos theory by economists people and by he financial community. Economists have not in general a lot of data, thus their approach is mainly theoretical: they consider analytical models and analyse their behaviour with respect o the evolution of the parameters. When chaotic behaviour can appear, they are interested to control it. In finance, working with intra daily data permit to have a lot of data and the approach is completely different. It is mainly experimental: people use non parametric tools. They try to detect chaotic behaviour inside data sets by the knowledge of an attractor. Thus, they need tests to detect the chaotic behaviour of their data. They need also to reconstruct orbits inside the attractor when it exists and to estimate the Lyapunov exponents which characterize the behaviour of the data.. When the attractor is determined (using embedding for instance) and the orbits well estimated, it is possible to make forecasts inside the attractor which is the main objective of the finance community using this approach. Short term forecasts can be easily obtained, but also long term forecasts. Indeed, chaotic systems as stochastic processes can present long memory behaviour with respect to the evolution of their autocorrelation function. Thus, it is possible to make long term forecasts inside an attractor. The question of mean term prediction is still opened. Another important problem concerns the deconvolution of the financial data which are strong noisy: an approach which seems promising is based on wavelets theory.