Forecasting the monthly retail sales of electricity based on the semi-functional linear model with autoregressive errors

In many statistical applications, data are collected sequentially over time and exhibit autocorrelation characteristics. Ignoring this autocorrelation may lead to a decrease in the model's prediction accuracy. To this end, assuming that the error process is an autoregressive process, this paper introduced a semi-functional linear model with autoregressive errors. Based on the functional principal component analysis and the spline method, we obtained the estimators of the slope function, nonparametric function, and autoregressive coefficients. Under some regular conditions, we found the convergence rate of the proposed estimators. A simulation study was conducted to investigate the finite sample performance of the proposed estimators. Finally, we applied our model to forecast the monthly retail sales of electricity, which illustrates the validity of our model from a predictive perspective.