Fractal assessment of wavelet based techniques for improving the predictions of the artificial neural network

Natural resources management including water resources requires reliable estimations of time variant environmental parameters. Small improvements in the estimation of environmental parameters would result in great effects on managing decisions. Noise reduction using wavelet techniques is an effective approach for preprocessing of practical data sets. More than 38 years monthly discharge time series of Ghar-e-Aghaj River in Iran are preprocessed using continuous and discrete wavelet transforms in this study. Predictability enhancement of the river flow time series are assessed using fractal approaches before and after applying wavelet based preprocessing. Time series correlation and persistency, the minimum sufficient length for training the predicting model and the maximum valid length of predictions were also investigated through a fractal assessment. A multi-layer perceptron neural network model was used as the predicting model. The performance evaluation criteria of the models depict the predictability enhancement of the preprocessed time series. The fractal based predictability index also depicted the improvement in the river flow time series prediction. A windowing fractal technique, as a new idea, is employed to evaluate the minimum sufficient length of time series needed for prediction and the maximum valid predicted length of the time series before and after the preprocessing. Results indicated that in case of using the processed time series, while the maximum valid lengths of predictions increase the minimum sufficient lengths for prediction decrease. Results also showed remarkable increase in the preprocessed time series correlation and persistency.