Although　the　classic　exponential-smoothing　models　and　grey　prediction　models　have　been　widely　used　in　time　series　forecasting,　this　paper　shows　that　they　are　susceptible　to　fluctuations　in　samples.　A　new　fractional　bidirectional　weakening　buffer　operator　for　time　series　prediction　is　proposed　in　this　paper.　This　new　operator　can　effectively　reduce　the　negative　impact　of　unavoidable　sample　fluctuations.　It　overcomes　limitations　of　existing　weakening　buffer　operators,　and　permits　better　control　of　fluctuations　from　the　entire　sample　period.　Due　to　its　good　performance　in　improving　stability　of　the　series　smoothness,　the　new　operator　can　better　capture　the　real　developing　trend　in　raw　data　and　improve　forecast　accuracy.　The　paper　then　proposes　a　novel　methodology　that　combines　the　new　bidirectional　weakening　buffer　operator　and　the　classic　grey　prediction　model.　Through　a　number　of　case　studies,　this　method　is　compared　with　several　classic　models,　such　as　the　exponential　smoothing　model　and　the　autoregressive　integrated　moving　average　model,　etc.　Values　of　three　error　measures　show　that　the　new　method　outperforms　other　methods,　especially　when　there　are　data　fluctuations　near　the　forecasting　horizon.　The　relative　advantages　of　the　new　method　on　small　sample　predictions　are　further　investigated.　Results　demonstrate　that　model　based　on　the　proposed　fractional　bidirectional　weakening　buffer　operator　has　higher　forecasting　accuracy.　©　2018　Elsevier　Inc.