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A combined forecast with weights adaptively selected and errors calibrated by Hidden Markov model (HMM) is proposed to model the day-ahead electricity price. Firstly several single models were built to forecast the electricity price separately. Then the validation errors from every individual model were transformed into two discrete sequences: an emission sequence and a state sequence to build the HMM, obtaining a transmission matrix and an emission matrix, representing the forecasting ability state of the individual models. The combining weights of the individual models were decided by the state transmission matrixes in HMM and the best predict sample ratio of each individual among all the models in the validation set. The individual forecasts were averaged to get the combining forecast with the weights obtained above. The residuals of combining forecast were calibrated by the possible error calculated by the emission matrix of HMM. A case study of day-ahead electricity market of Pennsylvania-New Jersey-Maryland (PJM), USA, suggests that the proposed method outperforms individual techniques of price forecasting, such as support vector machine (SVM), generalized regression neural networks (GRNN), day-ahead modeling, and self-organized map (SOM) similar days modeling

Electricity Price Forecast Using Combined Models with Adaptive Weights Selected and Errors Calibrated by Hidden Markov Model