Optimal determination of hidden Markov model parameters for fuzzy time series forecasting

Abstract

This paper presents Fuzzy Time Series (FTS) forecasting technique using Hidden Markov Model (HMM) optimized by Particle Swarm Optimization (PSO) and Genetic algorithm (GA). One of the major limitations of HMM is the lack of efficient method for HMM parameter estimation. Traditional methods like Baum Welch Algorithm (BWA) have been used to address the associated problem with HMM model. The BWA in itself does not truly capture the fuzziness in natural data resulting in the HMM algorithm into local minima. To address this challenge, this paper formulates the HMM parameter estimation problem into an optimization problem optimized by GA and PSO algorithms. To solve the problem of insufficiency in data allied with the HMM model, we adopted a method called smoothing to reduce the occurrence of zero in the observation events. Monte Carlo simulation is used at the end of the forecast to maintain stability and efficiency of the developed approach. The performance of developed model is evaluated using data of daily average temperature and cloud density of Taipei Taiwan, the Internet traffic data of Ahmadu Bello University (ABU) and Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX). Experimental results showed that the proposed forecasting models has a good forecasting accuracy when compared with existing models.

Keywords

• HMM
• Fuzzy Time Series
• Monte Carlo Simulation
• Baum Welch Algorithm
• Genetic Algorithm
• Particle Swarm Optimization