This paper proposes a forecasting framework that employs a seasonal autoregressive integrated moving average model with exogenous variables (main effects) and interaction variables (cross effects) to forecast hourly load demand data. The main effects and cross effects are measured through an iterative process of plotting, interpreting, and testing. Interactions of weather variables and calendar variables, as well as interactions of seasonal patterns and intraday dependencies, are analyzed, tested, and added to the model. The SARIMAX model, which contains only main effects, is compared with the SARIMAX model with interactions, which includes cross effects in addition to the main effects. The proposed SARIMAX model with interactions is shown to produce smaller errors than its competitors. That is, when considering the cross effects, the MAPE falls by 22.2% and the MAE and the RMSE fall by 21.3% and 21.8%, respectively. Thus, including interaction effects of the exogenous variables in the SARIMAX model can potentially improve the model's forecasting performance. Although the model is built using data for a specific region in Japan, the method is completely generic and therefore applicable to any load forecasting problem. (C) 2018 Elsevier Ltd. All rights reserved.