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Correlated time series refer to multiple time series which are recorded simultaneously to monitor the changing of multiple observations in a whole system. Correlated time series prediction plays a significant role in many real-world applications to help people make reasonable decisions. Yet it is very challenging, because different from single time series, correlated time series show both intra-sequence temporal dependencies and inter-sequence spatial dependencies. In addition, correlated time series are also affected by external factors in actual scenarios. Although RNNs have been proved to be effective on sequential data modeling, existing related works only focus on sequential patterns in a single time series, failing to comprehensively consider the inter-dependencies among multiple time series, which is essential for correlated time series prediction. In this paper, we propose a novel variant of LSTM, named CTS-LSTM, to collectively forecast correlated time series. Specifically, spatial and temporal correlations are explicitly modeled and respectively maintained in cells to capture the complex non-linear patterns in correlated time series. A general interface for handling external factors is further designed to enhance forecasting performance of the model. Experiments are conducted on two types of real-world datasets, viz., civil aviation passenger demand data and air quality data. And our CTS-LSTM achieves at least 9.0%, 16.5% and 21.3% lower RMSE, MAE and MAPE compared to the state-of-the-art baselines. [ABSTRACT FROM AUTHOR]