(A) study on chaotic attractor by locally weighted regression

Abstract

Recently, interest in deterministic chaotic dynamics has increased in the financial area. This has come about because the frequency of large moves in stock market is greater than would be expected under a normal distribution. Research on chaos can classify two-steps. One is to find evidence whether or not chaotic dynamics (i.e., chaotic attractor) exists. The other is to build a model that can explain chaotic attractor which was found in previous step. However, there was no research that gives satisfactory results. The purpose of this thesis is to find evidence of chaotic attractor and model that can explain chaotic attractor by connecting these two-steps. In this thesis, we contribute to a resolution of this disconnected step by building a model that explains chaotic attractor as dynamic equilibrium level with economic intuition. We address this issue by locally weighted regression in monthly stock returns.