HMM based Fuzzy Model for Time Series Prediction

This paper presents a hidden Markov model (HMM) based fuzzy rule extraction technique for predicting a time series generated by a chaotic dynamical system. The model uses three sequential phases. Firstly, the HMM is used to partition the input dataset based on the ordering of the calculated log-likelihood values (similarity measures). Then, a recursive top-down algorithm is used to generate the minimum number of rules required to accurately predict the next value in the time series using the training dataset. Finally, a gradient descent method is applied to the extracted fuzzy rules in order to fine-tune the model parameters. The performance of the proposed model is evaluated using a benchmark dataset -the Mackey-Glass time series. The results obtained clearly demonstrate significant improvement in prediction capabilities of the proposed HMM-fuzzy model when compared to the other techniques.