Abstract: In order to provide a reasonable criterion for the real-time analysis and short-term prediction of air traffic flow based on nonlinear theory, the stationarity and nonlinearity test methods of air traffic flow time series are studied. Firstly, the time series of traffic flow is constructed with 40-day data and 15-minute statistical interval; Then, the stability of the time series is analyzed by both qualitative method based on autocorrelation graph and quantitative method based on ADF(augmented Dickey-Fuller test) and PP(Phillips-Perron)test; Then, the non-linearity of the time series is studied by using surrogate data method; Finally, the effects of length, time delay and statistical scale on nonlinearity are analyzed. Results show that the autocorrelation coefficient of time series decreases rapidly and tends to zero, and there is no unit root in the generation process of time series data, which indicates that time series is stationary. The third -order time inverse asymmetry, third -order autocorrelation and third - order autocovariance are used as test statistics, and the third null hypothesis is rejected, which indicates that time series has a non-linear component, and the component originates from the dynamic process of the system itself. In addition, long-length time series often reflects more stable non-linearity, and short-length time series often does not reflect non -linearity. Time delay has a greater impact on the third -order statistics of time inverse asymmetry, but a smaller impact on the statistics. Time series with 30-minute scale is more suitable for shortterm prediction of Sanya No.4 Sector

Key words: air transportation, air traffic flow, stationarity, nonlinearity, time series