FORECASTING HOURLY ENERGY CONSUMPTION: IS FUNCTIONAL DATA ANALYSIS WORTH THE COMPLEXITY?

Abstract

This thesis compares an autoregressive Hilbertian model of order 1 (ARH(1)) with a classical two-step PCA+VAR(1) approach for forecasting daily electricity consumption curves. We use a year-long subset (Oct. 1, 2023 to Sept. 30, 2024) of the PJM Hourly Energy Consumption data across five areas. We additionally benchmark modern forecasting models including NHITS, a deep neural network, a recurrent LSTM model, and Nixtla’s TimeGPT (a pre-trained time-series Trans former). Each method predicts the next day’s 24-hour load curve from the current day’s curve, except TimeGPT, which generates forecasts based on the full historical context available up to each forecast origin. Forecast accuracy is evaluated via mean absolute error (MAE), mean squared error (MSE), and symmetric mean absolute percentage error (sMAPE). The ARH(1) and PCA+VAR(1) models show very similar performance and outperform the other methods on average. This was a surprising finding, suggesting that in this well-behaved data scenario, the functional approach offers little advantage over a simple PCA-based multivariate approach. To investigate further, we conduct a simplified experiment forecasting the next day’s average consumption using functional PCR (FPCR) vs. standard PCR. The results again show nearly identical performance from both methods. We hypothesize that when the functional data are densely and regularly sampled with no missing values, functional principal component analysis (FPCA) is essentially equivalent to ordinary PCA, and thus ARH(1) offers no clear improvement over PCA+VAR(1). We formalize this hypothesis and discuss conditions under which fully functional methods may still offer advantages (e.g. irregular sampling or complex functional structure). Finally, we propose directions for theoretical work to rigorously explain the observed equivalence.