A Hidden Markov Model-based fuzzy modeling of multivariate time series

This study elaborates on a novel Hidden Markov Model (HMM)-based fuzzy model for time series prediction. Fuzzy rules (rule-based models) are employed to describe and quantify the relationship between the input and output time series, while the HMM is regarded as a vehicle for efficiently capturing the temporal behavior or changes of the multivariate time series which are not capable to capture through commonly encountered fuzzy rule-based models. Essentially, the proposed strategies control the contribution of different fuzzy rules so that the proposed model can well model the dynamic behavior of time series. Fuzzy C-Means clustering technique is an alternative way to construct fuzzy rules. Particle swarm optimization serves as a tool to optimize the parameters of the model (e.g., transition matrix and emission matrix). We construct and investigate the performance of the HMM-based fuzzy model by using a series of synthetic and publicly available multivariate time series. Experimental results demonstrate that the proposed model shows better performance than the fuzzy rule-based models used without the involvement of HMMs.