Modeling Chaotic Time Series using Stochastic Differential Equation

In this paper, attempts were made to build an appropriate model for the prediction of chaotic time series by using Langevin equation. Langevin equation is a linear stochastic differential equation related to the world of time series and is called Ornstein-Uhlenbeck process. The OrnsteinUhlenbeck process is a Gaussian process with autocovariance and which can be transformed into state dependent time series model. The state dependent model can be reduced to an autoregressive integrated moving average (ARIMA) process or an autoregressive moving average (ARMA) process. The study of chaotic models is fascinating and this paper may contribute to the understanding of random behavior in time series modelling. (