Social media has been contributing many research areas such as data mining, recommender systems, time series analysis, etc. However, there are not many successful applications regarding social media in government agencies. In fact, lots of governments have social media accounts such as twitter and facebook. More and more customers are likely to communicate with governments on social media, causing massive external social media data for governments. This external data would be beneficial for analysing behaviours and real needs of the customers. Besides this, most governments also have a call centre to help customers solve their problems. It is not difficult to imagine that the enquiries on external social media and internal call centre may have some coupling relationships. The couplings could be helpful for studying customers’ intent and allocating government’s limited resources for better service. In this paper, we mainly focus on analysing the coupling relations between internal call centre and external public media using time series analysis methods for Australia Department of Immigration and Border Protection. The discovered couplings demonstrate that call centre and public media indeed have correlations, which are significant for understanding customers’ behaviours.