The impacts of outlying shocks on wind power time series are explored by considering the outlier effect in the volatility of wind power time series. A novel short term wind power forecasting method based on outlier smooth transition autoregressive (OSTAR) structure is advanced, then, combined with the generalized autoregressive conditional heteroskedasticity (GARCH) model, the OSTAR-GARCH model is proposed for wind power forecasting. The proposed model is further generalized to be with fat-tail distribution. Consequently, the mechanisms of regimes against different magnitude of shocks are investigated owing to the outlier effect parameters in the proposed models. Furthermore, the outlier effect is depicted by news impact curve (NIC) and a novel proposed regime switching index (RSI). Case studies based on practical data validate the feasibility of the proposed wind power forecasting method. From the forecast performance comparison of the OSTAR-GARCH models, the OSTAR-GARCH model with fat-tail distribution proves to be promising for wind power forecasting.