In this paper, we propose a heterogeneous federated learning (HFL) system for sparse time series prediction in healthcare, which is a decentralized federated learning algorithm with heterogeneous transfers. We design dense and sparse feature tensors to deal with the sparsity of data sources. Heterogeneous federated learning is developed to share asynchronous parts of networks and select appropriate models for knowledge transfer. Experimental results show that the proposed HFL achieves the lowest prediction error among all benchmark systems on eight out of ten prediction tasks, with MSE reduction of 94.8%, 48.3%, and 52.1% compared to the benchmark systems. These results demonstrate the effectiveness of HFL in transferring knowledge from heterogeneous domains, especially in the smaller target domain. Ablation studies then demonstrate the effectiveness of the designed mechanisms for heterogeneous domain selection and switching in predicting healthcare time series with privacy, model security, and heterogeneous knowledge transfer.