Hidden Markov Mixture of Gaussian Process Functional Regression: Utilizing Multi-Scale Structure for Time Series Forecasting

The mixture of Gaussian process functional regressions (GPFRs) assumes that there is a batch time series or sample curves are generated by independent random processes with different temporal structures. However, in real situations, these structures actually transferred manner from long scale. Therefore, the assumption not true practice. In order to get rid this limitation, we propose hidden-Markov-based GPFR model (HM-GPFR) describing both fine- and coarse-level Specifically, structure described at fine level hidden Markov coarse level. whole can be regarded as state switching dynamics. To further enhance robustness model, also give priori parameters develop Bayesian-hidden-Markov-based (BHM-GPFR). experimental results demonstrated proposed methods have high prediction accuracy good interpretability.