Advancing short-term load forecasting with decomposed Fourier ARIMA: A case study on the Greek energy market

Accurate short-term load forecasting (STLF) is crucial for the operational stability and efficiency of modern energy systems, particularly in markets experiencing increasing complexity. Traditional statistical methods, despite their robustness, often struggle to model multifrequency seasonality. This paper introduces a novel forecasting model, the decomposed Fourier ARIMA (FARIMA), designed to address multifrequency seasonal patterns in time series data with a specific application in this study to electricity consumption data. The FARIMA model combines Fourier decomposition to isolate periodic components, polynomial regression to capture trends, and ARIMA to model the residuals. The study evaluates optimal training periods and benchmarks FARIMA's performance against mature traditional methods, specifically SARIMA and Holt-Winters, which are widely used in short-term load forecasting. Using Greek energy market data, FARIMA consistently outperformed SARIMA and Holt-Winters across different setups. For a one-year training period, it achieved a MAPE that was 1.59 percentage points lower than SARIMA's and 1.44 percentage points lower than Holt-Winters'. For a six-month training period, FARIMA achieved a MAPE that was 0.17 percentage points lower than SARIMA's and 3.33 percentage points lower than Holt-Winters'. Additionally, FARIMA demonstrated significant computational efficiency, achieving a runtime reduction of 98.5 % compared to SARIMA in both setups, due to its ability to simplify residual signals and use less complex ARIMA parameters. Results demonstrate FARIMA's superior forecasting accuracy, specifically for one-week-ahead predictions, with lower Mean Absolute Percentage Error (MAPE) and Root Mean Squared Error (RMSE) compared to conventional models. The FARIMA model bridges gaps in traditional forecasting by effectively capturing multifrequency patterns. While its practical implications primarily focus on short-term load forecasting, for which it was specifically developed, FARIMA is fundamentally a new time series model. As such, it holds potential for application across a wide range of domains involving multifrequency time series data.