Chaotic Time Series Prediction Using Optimal Fuzzy Systems Based on Sequential Quadratic Programming-Case Study: Gold Price

This paper presents a fuzzy approach to the prediction of highly nonlinear timeseries.The optimized Mamdani-type fuzzy system denoted SQP-FLC is applied forthe input-output modeling of measured data. In order to tune fuzzy membershipfunctions, a sequential quadratic programming (SQP) method is employed. Theproposed method is evaluated and validated on a highly complex time series, dailygold price data. The time series is primarily investigated for its chaotic properties.Correlation dimension and autocorrelation function (ACF) for the time series arediscussed. Accordingly, time delay and embedding dimension are computed. Monthselection in each stage is based on computed correlation coefficients. Thus, for theproposed fuzzy predictor, 3, 5, and 7 dynamics are selected and the time series areverified. The simulation results for one-step-ahead prediction of daily gold price in2010, compared with methods of ANFIS and GA-FLC, demonstrate comparablybetter performance of the proposed SQP-FLC until the higher significant dynamicsof the chaotic trend is taken into account.

Keywords:

Chaotic Time Series , Complex Systems , Mamdani-Type Fuzzy Modeling , Optimization , Sequential Quadratic Programming