Nonlinear Dynamics and Chaos: Application to Financial Markets in Pakistan (The Pakistan Development Review, 1994)
Recently there has been an increased interest in the theory of chaos by macroeconomists and fmancial economists. Originating in the natural sciences, applications of the theory have spread through various fields including brain research, optics, metereology, and economics. The attractiveness of chaotic dynamics is its ability to generate large movements which appear to be random, with greater frequency than linear models. Two of the most striking features of any macro-economic data are its random-like appearance and its seemingly cyclical character. Cycles in economic data have often been noticed, from short-run business cycles, to 50 years Kodratiev waves. There have been many attempts to explain them, e.g. Lucas (1975), who argues that random shocks combined with various lags can give rise to phenomena which have the appearance of cycles, and Samuelson (1939) who uses the familiar multiplier accelerator model. The advantage of using non-linear difference (or differential) equation models to explain the business cycle is that it does not have to rely on ad hoc unexplained exogenous random shocks.