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Accumulation of influencing factors during several consecutive time periods makes the variation of target parameters lag behind the variation of their influencing factors. This important phenomenon, known as the cumulative effect, would lead to relatively large forecasting errors. In this paper, the dynamic similar sub-series method is proposed to take cumulative effect into consideration. The similar sub-series for the forecasting parameter sub-series are selected based on similarities of target parameter sub-series and influencing factors sub-series. The internal variations of target parameter sub-series and each influencing factor sub-series are innovatively integrated into the selection rules for the dynamic similar sub-series. The corresponding forecasting algorithm is designed, and the forecasting parameters are deduced and forecasted according to the variation of the dynamic similar sub-series. The proposed method is compared with a variety of representative methods under the short-term daily average load forecasting, the electricity price forecasting and the global horizontal irradiance forecasting scenarios to demonstrate its effectiveness.