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• CSI-SVQR is proposed for wind power probability density forecasting. • Cubic spline interpolation is used to reduce the noisy of wind power data. • The optimal CWC criterion is used to acquire the best PIs. • The SSE of mode criterion is used to acquire the best point forecasting results. • Wilcoxon test verifies that CSI improves the accuracy of forecasting methods. Accurate forecasting of wind power plays an important role in an effective and reliable power system. However, the fact of non-schedulability and fluctuation of wind power significantly increases the uncertainty of power systems. The output power of a wind farm is usually mixed with uncertainties, which reduce the effectiveness and accuracy of wind power forecasting. In order to handle the uncertainty of wind power, this paper first proposes to conduct outlier detection and reconstruct data before the prediction. Then, a wind power probability density forecasting method is proposed, based on cubic spline interpolation and support vector quantile regression (CSI-SVQR), which can better estimate the whole wind power probability density curve. However, the probability density prediction method can not acquire the optimal point prediction and interval prediction results at the same time. In order to analyze the uncertainty of wind power, the present study considers the prediction results from the perspective of probabilistic point prediction and interval prediction respectively. Three sets of real-world wind power data from Canada and China are used to validate the CSI-SVQR method. The results show that the proposed method not only efficiently eliminates the outliers of wind power but also provides the probability density function, offering a complete description of wind power generation fluctuation. Furthermore, more accurate point prediction and prediction interval (PI) can be obtained compared to existing methods. Wilcoxon signed rank test is used to verify that CSI can improve the performance of forecasting methods. [ABSTRACT FROM AUTHOR]