Multiscale complexity analysis on airport air traffic flow volume time series

Exploring the complexity of airport air traffic flow volume time series helps gain insights into the evolution mechanism of the air traffic system. To obtain more reliable and stable entropy values, we introduce multiple coarse-graining procedures into the multivariate multiscale permutation entropy (MMPE) method to propose an improved MMPE (IMMPE) method to explore multivariate time series. By introducing similar multiple coarse-graining procedures, we also improve the contingency to investigate the inhomogeneity level between ordinal pattern distributions in multivariate time series. With the improved multiscale permutation entropy (IMPE) method, firstly, we investigate the complexity of the departure and the arrival air traffic flow volume time series of the top ten busiest airports in China from a univariate time series perspective. Then, with IMPE and IMMPE, we investigate the complexity of the total air traffic flow volume time series of the ten airports from a univariate and a multivariate time series perspective, respectively. Results show that the complexity is dependent on the time scale, and thus it is necessary to conduct multiscale analysis on the complexity. Benefiting from the improvement in IMPE and IMMPE, on the reliable and stable entropy curves, we can exactly explore and locate sharp decreasing points of the entropy values to reveal severe fluctuations of the multiscale complexity of the time series. Gaps between IMPE and IMMPE curves of the total air traffic flow volume time series indicate the necessity of analyzing the time series from the multivariate time series perspective. Moreover, spikes on the improved contingency curves reveal that the inhomogeneity level between fluctuations of the departure and the arrival air traffic flows is also scale-dependent, and the maxima are all located on the scale 72 (6 hours).