Purpose:　The　purpose　of　this　paper　is　to　solve　the　problems　existing　in　topic　popularity　prediction　in　online　social　networks　and　advance　a　fine-grained　and　long-term　prediction　model　for　lack　of　sufficient　data.　Design/methodology/approach:　Based　on　GM(1,1)　and　neural　networks,　a　co-training　model　for　topic　tendency　prediction　is　proposed　in　this　paper.　The　interpolation　based　on　GM(1,1)　is　employed　to　generate　fine-grained　prediction　values　of　topic　popularity　time　series　and　two　neural　network　models　are　considered　to　achieve　convergence　by　transmitting　training　parameters　via　their　loss　functions.　Findings:　The　experiment　results　indicate　that　the　integrated　model　can　effectively　predict　dense　sequence　with　higher　performance　than　other　algorithms,　such　as　NN　and　RBF_LSSVM.　Furthermore,　the　Markov　chain　state　transition　probability　matrix　model　is　used　to　improve　the　prediction　results.　Practical　implications:　Fine-grained　and　long-term　topic　popularity　prediction,　further　improvement　could　be　made　by　predicting　any　interpolation　in　the　time　interval　of　popularity　data　points.　Originality/value:　The　paper　succeeds　in　constructing　a　co-training　model　with　GM(1,1)　and　neural　networks.　Markov　chain　state　transition　probability　matrix　is　deployed　for　further　improvement　of　popularity　tendency　prediction.　©　2020,　Emerald　Publishing　Limited.