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

Abstract

This paper presents a fuzzy approach to the prediction of highly nonlinear timeseries. The optimized Mamdani-type fuzzy system denoted SQP-FLC is applied for the input-output modeling of measured data. In order to tune fuzzy membership functions, a sequential quadratic programming (SQP) method is employed. The proposed method is evaluated and validated on a highly complex time series, daily gold price data. The time series is primarily investigated for its chaotic properties. Correlation dimension and autocorrelation function (ACF) for the time series are discussed. Accordingly, time delay and embedding dimension are computed. Month selection in each stage is based on computed correlation coefficients. Thus, for the proposed fuzzy predictor, 3, 5, and 7 dynamics are selected and the time series are verified. The simulation results for one-step-ahead prediction of daily gold price in 2010, compared with methods of ANFIS and GA-FLC, demonstrate comparably better performance of the proposed SQP-FLC until the higher significant dynamics of the chaotic trend is taken into account.