Thermostatically-controlled loads have a significant impact on electricity demand after service is restored following an outage, a phenomenon known as cold load pick-up. Widespread deployment of smart metering devices is also opening up new opportunities for data-driven load modelling and prediction. In this paper, we propose an architecture for local estimation of cold load pick-up using time-stamped local load measurements. The proposed approach uses ARIMA modelling for short-term foregone energy consumption prediction during an outage. Predictions are made on a hourly basis to estimate the energy to potentially recover after outages lasting up to several hours. Moreover, to account for changing customer behavior and weather, the model order is adjusted dynamically. Simulation results based on actual smart meter measurements are presented for 50 residential customers over the duration of one year. These results are then validated using physical modelling of residential loads and match well ARIMA-based predictions.