Smart homes, powered mostly by Internet of Things (IoT) devices, have become very popular nowadays due to their ability to provide a holistic approach towards effective energy management. This is made feasible via the deployment of multiple sensors, which enables predicting energy consumption via machine learning approaches. In this work, we propose FedTime, a novel federated learning approach for predicting smart home consumption which takes into consideration the age of the time series datasets of each client. The proposed method is based on federated averaging but aggregates local models trained on each smart home device to produce a global prediction model via a novel weighting scheme. Each local model contributes more to the global model when the local data are more recent, or penalized when the data are older upon testing for a specific residence (client). The approach was evaluated on a real-world dataset of smart home energy consumption and compared with other machine learning models. The results demonstrate that the proposed method performs similarly or better than other models in terms of prediction error; FedTime achieved a lower mean absolute error of 0.25 compared to FedAvg. The contributions of this work present a novel federated learning approach that takes into consideration the age of the datasets that belong to the clients, experimenting with a publicly available dataset on grid import consumption prediction, while comparing with centralized and decentralized baselines, without the need for data centralization, which is a privacy concern for many households.