Research papersThe incorrect usage of singular spectral analysis and discrete wavelet transform in hybrid models to predict hydrological time series

- Series generated by SSA and DWT contain information of 'future' values.
- Hybrid models generate false 'low' prediction error and cause large errors in test.
- In literature the usage of SSA and DWT in building hybrid models is incorrect.

In hydrological time series prediction, singular spectrum analysis (SSA) and discrete wavelet transform (DWT) are widely used as preprocessing techniques for artificial neural network (ANN) and support vector machine (SVM) predictors. These hybrid or ensemble models seem to largely reduce the prediction error. In current literature researchers apply these techniques to the whole observed time series and then obtain a set of reconstructed or decomposed time series as inputs to ANN or SVM. However, through two comparative experiments and mathematical deduction we found the usage of SSA and DWT in building hybrid models is incorrect. Since SSA and DWT adopt 'future' values to perform the calculation, the series generated by SSA reconstruction or DWT decomposition contain information of 'future' values. These hybrid models caused incorrect 'high' prediction performance and may cause large errors in practice.