In this paper a semi-parametric approach is developed to model non-linear relationships in time series data. The nonlinearity is modeled using regression splines, which are computationally very efficient in comparison with many other nonparametric methods. This is especially relevant in short-term forecasting. With an explicit functional form, the results obtained with regression splines are also more interpretable. The serial correlation contained in the random error is captured using an ARMA model. The estimation procedure is developed, and the selection of smoothing parameters is discussed. In this paper this approach is used to forecast hourly electricity demand in a large residential area. The model considers the highly nonlinear effect of temperature, combined with those of time-of-day and type-of-day, and the seasonal correlation is modeled using an ARIMA model. Forecasting performance is evaluated by post-sample forecasting and comparative results are presented.