Hidden Markov Models Based Approaches to Long-Term Prediction for Granular Time Series

In time series forecasting, a challenging and important task is to realize long-term forecasting that is both accurate and transparent. In this study, we propose a long-term prediction approach by transforming the original numerical data into some meaningful and interpretable entities following the principle of justifiable granularity. The obtained sequences exhibiting sound semantics may have different lengths, which bring some difficulties when carrying out predictions. To equalize these temporal sequences, we propose to adjust their lengths by involving the dynamic time warping (DTW) distance. Two theorems are included to ensure the correctness of the proposed equalization approach. Finally, we exploit hidden Markov models (HMM) to derive the relations existing in the granular time series. A series of experiments using publicly available data are conducted to assess the performance of the proposed prediction method. The comparative analysis demonstrates the performance of the prediction delivered by the proposed model.