  Various probabilistic time series forecasting models have sprung up and shown
remarkably good performance. However, the choice of model highly relies on the
characteristics of the input time series and the fixed distribution that the
model is based on. Due to the fact that the probability distributions cannot be
averaged over different models straightforwardly, the current time series model
ensemble methods cannot be directly applied to improve the robustness and
accuracy of forecasting. To address this issue, we propose pTSE, a multi-model
distribution ensemble method for probabilistic forecasting based on Hidden
Markov Model (HMM). pTSE only takes off-the-shelf outputs from member models
without requiring further information about each model. Besides, we provide a
complete theoretical analysis of pTSE to prove that the empirical distribution
of time series subject to an HMM will converge to the stationary distribution
almost surely. Experiments on benchmarks show the superiority of pTSE overall
member models and competitive ensemble methods.
