A new hybrid adaptive autoregressive moving average (ARMA) and functional link neural network (FLNN) trained by adaptive cubature Kalman filter (ACKF) is presented in this paper for forecasting day-ahead mixed short-term demand and electricity prices in smart grids. The hybrid forecasting framework is intended to capture the dynamic interaction between the electricity consumers and the forecasted prices resulting in the shift of demand curve in electricity market. The proposed model comprises a linear ARMA-FLNN obtained by using a nonlinear expansion of the weighted inputs. The nonlinear functional block helps introduce nonlinearity by expanding the input space to higher dimensional space through basis functions. To train the ARMA-FLNN, an ACKF is used to obtain faster convergence and higher forecasting accuracy. The proposed method is tested on several electricity markets, and the performance metrics such as the mean average percentage error (MAPE), and error variance are compared with other forecasting methods, indicating the improved accuracy of the approach and its suitability for a real-time forecasting.