This paper examines the potential impact of automatic meter reading (AMR) on short-term load forecasting for a residential customer. Real-time measurement data from customers' smart meters provided by a utility company is modeled as the sum of a deterministic component and a Gaussian noise signal. The shaping filter for the Gaussian noise is calculated using spectral analysis. Kalman filtering is then used for load prediction. The accuracy of the proposed method is evaluated for different sampling periods and planning horizons. The results show that the availability of more real-time measurement data improves the accuracy of the load forecast significantly. However, the improved prediction accuracy can come at a high computational cost. Our results qualitatively demonstrate that achieving the desired prediction accuracy while avoiding a high computational load requires limiting the volume of data used for prediction. Consequently, the measurement sampling rate must be carefully selected as a compromise between these two conflicting requirements.