Deep　learning　is　well-known　for　extracting　high-level　abstract　features　from　a　large　amount　of　raw　data　without　relying　on　prior　knowledge,　which　is　potentially　attractive　in　forecasting　financial　time　series.　Long　short-term　memory　(LSTM)　networks　are　deemed　as　state-of-the-art　techniques　in　sequence　learning,　which　are　less　commonly　applied　to　financial　time　series　predictions,　yet　inherently　suitable　for　this　domain.　We　propose　a　novel　methodology　of　deep　learning　prediction,　and　based　on　this,　construct　a　deep　learning　hybrid　prediction　model　for　stock　markets-CEEMD-PCA-LSTM.　In　this　model,　complementary　ensemble　empirical　mode　decomposition　(CEEMD),　as　a　sequence　smoothing　and　decomposition　module,　can　decompose　the　fluctuations　or　trends　of　different　scales　of　time　series　step　by　step,　generating　a　series　of　intrinsic　mode　functions　(IMFs)　with　different　characteristic　scales.　Then,　with　retaining　the　most　of　information　on　raw　data,　PCA　reduces　dimension　of　the　decomposed　IMFs　component,　eliminating　the　redundant　information　and　improving　prediction　response　speed.　After　that,　high-level　abstract　features　are　separately　fed　into　LSTM　networks　to　predict　closing　price　of　the　next　trading　day　for　each　component.　Finally,　synthesizing　the　predicted　values　of　individual　components　is　utilized　to　obtain　a　final　predicted　value.　The　empirical　results　of　six　representative　stock　indices　from　three　types　of　markets　indicate　that　our　proposed　model　outperforms　benchmark　models　in　terms　of　predictive　accuracy,　i.e.,　lower　test　error　and　higher　directional　symmetry.　Leveraging　key　research　findings,　we　perform　trading　simulations　to　validate　that　the　proposed　model　outperforms　benchmark　models　in　both　absolute　profitability　performance　and　risk-adjusted　profitability　performance.　Furthermore,　model　robustness　test　unveils　the　more　stable　robustness　compared　to　benchmark　models.　(C)　2020　Elsevier　Ltd.　All　rights　reserved.