In 2015, the Ministry of Land, Infrastructure and Transportation started to provide information on aircraft flying over Japan, called CARATS Open Data, and to promote research on aviation systems actively. The airspace is divided into sectors, which are used for limiting air traffic to control safely and efficiently. Since the demand for air transportation is increasing, new optimization techniques and efficient control have been required to predict and resolve demand-capacity imbalances in the airspace. In this paper, we aim to construct mathematical models of the inter-sector air traffic flow from CARATS Open Data. In addition, we develop methods to predict future sector demand. Accuracy of the prediction is evaluated by comparison between predicted sector demand and the actual data.