Forecasting day-ahead electric power prices with functional data analysis

Day-ahead electricity prices in today’s competitive electric power markets have complex features such as high frequency, high volatility, non-linearity, non-stationarity, mean reversion, multiple periodicities, and calendar effects. These complicated features make price forecasting difficult. To address this, this research examines the application of functional data analysis to forecasting day-ahead electric power prices. Compared to classical time series forecasting approaches, functional data analysis is more appealing since it anticipates the daily profile, allowing for short-term projections. This technique uses a functional autoregressive ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m1"><mml:mrow><mml:mi mathvariant="double-struck">F</mml:mi></mml:mrow></mml:math> AR) and a functional autoregressive with exogenous predictors ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m2"><mml:mrow><mml:mi mathvariant="double-struck">F</mml:mi></mml:mrow></mml:math> AR <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m3"><mml:mrow><mml:mi mathvariant="double-struck">X</mml:mi></mml:mrow></mml:math> ) model to predict the next-day electric power prices. In addition, standard time-series forecasting models, including autoregressive (AR) AR <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m4"><mml:mrow><mml:mi mathvariant="double-struck">X</mml:mi></mml:mrow></mml:math> , autoregressive integrated moving average (ARIMA), and ARIMA <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m5"><mml:mrow><mml:mi mathvariant="double-struck">X</mml:mi></mml:mrow></mml:math> are also utilized for comparison. The model’s prediction performance was evaluated using data on electricity prices from the British electricity market, considering forecast error indicators and the same forecast statistical test. The results show that the proposed functional models ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m6"><mml:mrow><mml:mi mathvariant="double-struck">F</mml:mi></mml:mrow></mml:math> AR and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m7"><mml:mrow><mml:mi mathvariant="double-struck">F</mml:mi></mml:mrow></mml:math> AR <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m8"><mml:mrow><mml:mi mathvariant="double-struck">X</mml:mi></mml:mrow></mml:math> ) outperform standard time series models. In comparison to the benchmark models (AR, AR <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m9"><mml:mrow><mml:mi mathvariant="double-struck">X</mml:mi></mml:mrow></mml:math> , ARIMA, ARIMA <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m10"><mml:mrow><mml:mi mathvariant="double-struck">X</mml:mi></mml:mrow></mml:math> , and the proposed <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m11"><mml:mrow><mml:mi mathvariant="double-struck">F</mml:mi></mml:mrow></mml:math> AR model), the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m12"><mml:mrow><mml:mi mathvariant="double-struck">F</mml:mi></mml:mrow></mml:math> AR <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m13"><mml:mrow><mml:mi mathvariant="double-struck">X</mml:mi></mml:mrow></mml:math> model reduces: the day-ahead forecasting average MAPE by ranges of 5.02%–45.77%, 4.07%–40.63%, 3.80%–38.99%, 1.90%–24.22%, and 0.95%–13.78%; MAE by ranges of 9.43%–69.32%, 5.17%–65.48%, 6.04%–59.16%, 3.02%–42.01%, and 1.51%–26.59%; RMSE by ranges of 8.98%–40.97%, 6.68%–34.03%, 4.22%–24.58%, 3.91%–23.20%, and 2.30%–15.11%. Furthermore, compared with the literature-proposed best models, the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m14"><mml:mrow><mml:mi mathvariant="double-struck">F</mml:mi></mml:mrow></mml:math> AR <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m15"><mml:mrow><mml:mi mathvariant="double-struck">X</mml:mi></mml:mrow></mml:math> model produces a significantly higher accuracy and efficient day-ahead forecast based on forecasting error indicators and an equal forecast statistical test. Furthermore, compared with the best models proposed in the literature, the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m16"><mml:mrow><mml:mi mathvariant="double-struck">F</mml:mi></mml:mrow></mml:math> AR <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m17"><mml:mrow><mml:mi mathvariant="double-struck">X</mml:mi></mml:mrow></mml:math> model demonstrates significantly higher accuracy and efficiency in day-ahead forecasting, as evidenced by forecasting error indicators and an equal forecast statistical test.