Diagnosing Chaos in the Logistic Family of Discrete Market Dynamical Models

Abstract

We describe and illustrate a method for detecting chaotic behaviour in marketing time series data, and for estimating the value of parameters in underlying driving equations. The procedure is based on trajectory predictions and innovation sequence tests using the local overall model test (LOMT) method in the standard Kalman filter. The effectiveness of the detection method is tested using artificial time series data generated from a logistic model of market dynamics that is known to produce chaotic behaviour under certain conditions to which various degrees of random noise is added. The results show that the technique can convincingly detect chaotic behaviour in the generated time series data and future developments are discussed.