Joint Tensor Expectile Regression for Electricity Day-Ahead Price Curves

Forecasting of electricity day-ahead prices has become an important field in recent research due to the tremendous increase in unpredictable renewable power in-feed to the electricity systems. We propose new methodology that is able to capture the intraday structure and the structural brake from working days to weekends incorporated in a functional tensor expectile regression that deploys factorisation for dimension reduction and joint estimation of the coefficient space employing trust region optimisation. Our model captures the common and individual structure among and between the weekdays, respectively. Moreover, in contrast to standard literature, our model does not disrupt the continuity of time as the daily intraday price curves are treated as one observation. We apply our methodology to German electricity prices that show high volatility and negative prices since the strong penetration of renewable power. The EPEXSPOT price data is merged with time series data for electricity load forecasts and renewable forecasts. Further, the out-of-sample forecasting results indicate outperformance of our candidate model over standard practice