The　accurate　forecast　of　air　cargo　demand　is　essential　for　infrastructure　construction　planning　and　daily　operation　management.　Evidently,　it　is　extremely　difficult　to　capture　the　dynamics　of　time　series　impacted　by　distinct　sources.　To　reduce　the　complexity　of　data,　the　current　popular　method　is　to　decompose　the　original　data　into　several　modal　branches　with　different　characteristic　attributes.　But　the　new　problem　is　that　the　components　generated　by　decomposition　are　still　irregular　and　unstable,　and　there　is　no　unified　method　to　predict　them.　In　this　paper,　a　new　secondary　decomposition-ensemble　(SDE)　approach　with　a　cuckoo　search　algorithm　(CSA)　is　proposed　for　air　cargo　forecasting.　More　specifically,　the　original　air　cargo　time　series　is　decomposed　into　several　components　by　an　enhanced　decomposition　formwork,　which　consists　of　variational　mode　decomposition　(VMD),　sample　entropy　(SE)　and　empirical　mode　decomposition　(EMD).　Subsequently,　the　ARIMA　and　the　Elman　neural　networks　(ENN)　optimized　by　CSA　are　respectively　applied　to　forecast　the　trend　component　and　the　low-frequency　components,　during　which　the　phase　space　reconstruction　(PSR)　is　conducted　to　determine　the　input　structure　of　neural　networks.　The　final　forecasting　results　are　obtained　by　integrating　the　predicted　values　of　each　component.　Besides,　the　air　cargo　series　from　three　different　airports　in　China　are　adopted　to　validate　the　performance　of　our　proposed　approach　and　the　empirical　results　show　that　it　is　superior　to　all　other　benchmark　models　in　terms　of　the　robustness　and　accuracy.　(C)　2020　Elsevier　B.V.　All　rights　reserved.