Spatiotemporal　graph　neural　networks　(GNNs)　have　been　used　successfully　in　traffic　prediction　in　recent　years,　primarily　owing　to　their　ability　to　model　complex　spatiotemporal　dependencies　within　irregular　traffic　networks.　However,　the　feature　extraction　processes　in　these　methods　are　limited　in　their　exploration　of　the　inner　properties　of　traffic　data.　Specifically,　graph　and　temporal　convolutions　are　local　operations　and　can　hardly　utilize　information　from　wider　ranges,　which　may　affect　the　long-term　prediction　performance　of　such　methods.　Furthermore,　deep　spatiotemporal　GNNs　easily　suffer　from　poor　generalization　owing　to　overfitting.　To　address　these　problems,　this　study　presents　a　novel　traffic　prediction　method　that　integrates　self-supervised　learning　and　self-distillation　into　spatiotemporal　GNNs.　First,　a　self-supervised　learning　module　is　used　to　explore　the　knowledge　from　the　input　data.　An　auxiliary　task　based　on　temporal　continuity　is　designed　to　capture　the　contextual　information　in　traffic　data.　Second,　a　self-distillation　framework　is　developed　as　an　implicit　regularization　approach　that　transfers　knowledge　from　the　model　itself.　The　combination　of　self-supervision　and　self-distillation　further　mines　the　knowledge　from　the　data　and　the　model,　and　the　generalization　ability　and　stability　of　the　prediction　model　can　be　improved.　The　proposed　model　achieved　superior　or　competitive　results　compared　with　several　strong　baselines　on　six　traffic　prediction　datasets.　In　particular,　the　maximum　performance　improvement　ratios　for　the　six　datasets　were　3.0%　(MAE),　5.2%　(RMSE),　and　3.8%　(MAPE).　These　results　demonstrate　the　effectiveness　of　the　proposed　method.