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Hybrid BPNN-weighted grey-C3LSP (BWGC) prediction has been introduced earlier to overcome the crucial problem of overshooting phenomenon. However, some predicted values have been shown not precisely enough as the observations are really far away from both GM(1,1|α) and cumulated 3 points least squared linear prediction (C3LSP) outputs. Therefore, this study proposes a new prediction approach, incorporating non-linear generalized conditional heteroscedasticity (NGARCH) to integrate hybrid BPNN-weighted grey-C3LSP prediction, in which the smoothness of the final predicted output has been improved. In this way, the model's generalization is enhanced so as to further improve the prediction accuracy. The proposed method is verified successfully by two empirical experiments.