A hybrid linear–nonlinear approach to predict the monthly rainfall over the Urmia Lake watershed using wavelet-SARIMAX-LSSVM conjugated model

The present study aimed to develop a hybrid model to predict the rainfall time series of Urmia Lake watershed. For this purpose, a model based on discrete wavelet transform, ARIMAX and least squares support vector machine (LSSVM) (W-S-LSSVM) was developed. The proposed model was designed to handle linear, nonlinear and seasonality of rainfall time series. In the proposed model, time series were decomposed into sub-series (approximation (a) and details (d)). Next, the sub-series were predicted separately. In the proposed model, sub-series were fed into SARIMAX to be predicted. The residual of predicted sub-series (error) of the rainfall time series was then fed into LSSVM to predict the residual components. Then, all predicted values were aggregated to rebuild the predicted time series. In order to compare results, first a classic modeling was performed by LSSVM. Later, wavelet-based LSSVM was used to capture the peak values of rainfall. Results revealed that Daubechies 4 and decomposition level 4 (db(4,4)) led to the best outcome. Due to the performance of db(4,4), it was selected to be applied in the proposed model. Based on results, it was observed that the W-S-LSSVM's performance was improved in comparison with other models.