Averaging Predictive Distributions Across Calibration Windows for Day-Ahead Electricity Price Forecasting

Abstract

The recent developments in combining point forecasts of day-ahead electricity prices across calibration windows have provided an extremely simple, yet a very efficient tool for improving predictive accuracy. Here, we consider two novel extensions of this concept to probabilistic forecasting: one based on Quantile Regression Averaging (QRA) applied to a set of point forecasts obtained for different calibration windows, the other on a technique dubbed Quantile Regression Machine (QRM), which first averages these point predictions, then applies quantile regression to the combined forecast. Once computed, we combine the probabilistic forecasts across calibration windows by averaging probabilities of the corresponding predictive distributions. Our results show that QRM is not only computationally more efficient, but also yields significantly more accurate distributional predictions, as measured by the aggregate pinball score and the test of conditional predictive ability. Moreover, combining probabilistic forecasts brings further significant accuracy gains.

Energy Forecasting: A Review and Outlook

“…Ensemble forecasting methods have also been applied to smart meter data [38] and other subdomains of energy forecasting, such as price forecasting [39]- [41]. Empirical results show that for both point and probabilistic forecasts the quality of predictions can be significantly improved if combined, even when forecasts of the same model are averaged just across a few short and a few long calibration windows [42], [43].…”

PCA Forecast Averaging—Predicting Day-Ahead and Intraday Electricity Prices

“…Moreover, recently [18,19] show that also the averaging of predictions obtained with the same model but calibrated to a different portion of data improves the predictive accuracy. In the recent papers [18][19][20] regarding averaging forecasts across calibration windows of different lengths, authors argue that combining forecasts from only a number of carefully selected calibration windows can significantly increase the forecasting performance and outperform the average of all predictions. Authors show that both for point [18,19] and probabilistic forecasts [20], considering the mix of short and long calibration windows brings statistically significant gains in terms of the forecasting accuracy.…”

Regularized quantile regression averaging for probabilistic electricity price forecasting

“…Following the unprecedented success in the Global Energy Forecasting Competition 2014, QRA became a popular technique for probabilistic energy forecasting (see, e.g., Zhang et al, 2016;Liu et al, 2017;Zhang et al, 2018;Kostrzewski and Kostrzewska, 2019;Mpfumali et al, 2019;Serafin et al, 2019;Uniejewski et al, 2019;Wang et al, 2019). However, a recent study of Marcjasz et al (2020) has revealed the method's vulnerability to low quality predictors when the set of regressors is larger than just a few.…”

“…As in Section 4.2.3, we perform the CPA test of Giacomini and White (2006) only for the three well performing benchmarks (Q-Ave, F-Ave, QRM) and LQRA with three well performing values of λ. In Figure 7 we illustrate the obtained p-values using 'chessboards' (analogously as in Serafin et al, 2019), i.e., we use a heat map to indicate the range of the p-values -the closer they are to zero (→ dark green) the more significant is the difference between the forecasts of a model on the X-axis (better) and the forecasts of a model on the Y-axis (worse). Evidently, the CPA test results confirm and emphasize the observations made in Section 4.2.4.…”