Forecasting of hydrologic time series with ridge regression in feature space

Support vector machine (SVM) is one of the most elegant data mining engines developed most recently. It has been shown in various studies that SVM provides higher accuracy level than the local model in the chaotic time series analysis. Chaotic time series analysis usually requires a long data record and it is therefore computationally time consuming in addition to possible storage capacity problems. In this study a ridge linear regression is applied in a feature space. The feature space dimension of Gaussian kernel is infinite. With the use of a data sample set, the number of dimensions of feature space of Gaussian kernel can be estimated. The scheme can computationally be guaranteed to be faster and, at the same time, stable while the accuracy remains close to or much better than other existing techniques. Existing techniques used for comparisons are: (1) standard chaos technique; (2) Naive; (3) ARIMA; (4) Inverse Approach; and (5) SVM coupled the decomposition method. The parameters involved are calibrated with an evolutionary algorithm, Shuffled Complex Evolution (SCE). The performance of the proposed method is tested on Tryggevaelde catchment runoff and Mississippi river flow. Significantly higher prediction accuracies are obtained from the proposed scheme than from other existing techniques. In addition, the training speed of the scheme is very much faster than that of its counterparts (197 words < 300 words).