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.