In　recent　years,　artificial　neural　networks　(ANNs)　have　been　successfully　and　widely　used　in　multivariate　time　series　prediction,　but　the　accuracy　of　the　prediction　is　significantly　affected　by　the　ANNs’　input.　In　order　to　determine　the　appropriate　input　for　more　accurate　prediction,　a　weighted　slow　feature　analysis-based　adaptive　feature　extraction　(WSFA-AFE)　method　is　proposed　for　multivariate　time　series　prediction.　Firstly,　the　weighted　SFA　(WSFA)　algorithm　is　developed　to　extract　slow　features　weighted　by　their　contributions.　Then,　an　improved　adaptive　sliding　window　algorithm　is　designed　to　self-determine　the　historical　information　of　slow　features　for　input.　Finally,　the　out-of-model　performance　of　the　WSFA-AFE　method　is　verified　by　applying　it　to　different　ANN　models　with　several　benchmark　data　sets　as　well　as　a　practical　dataset　in　wastewater　treatment　process.　The　results　indicate　that　a　better　modeling　performance　of　ANNs　for　multivariate　time　series　prediction　can　be　obtained　by　the　WSFA-AFE　method,　which　can　adaptively　extract　feature　variables　from　the　multivariate　time　series.　Besides,　the　robustness　of　the　proposed　method　is　demonstrated　as　well.　©　2023,　The　Author(s),　under　exclusive　licence　to　Springer-Verlag　London　Ltd.,　part　of　Springer　Nature.