Investigation of denoising effects on forecasting models by statistical and nonlinear dynamic analysis

Abstract

In this study, the denoising effect on the performance of prediction models is evaluated. The 13-year daily data (2002–2015) of hydrological time series for the sub-basin of Parishan Lake of the Helle Basin in Iran were used to predict time series. At first, based on observational precipitation and temperature data, the prediction was performed, using the ARIMA, ANN-MLP, RBF, QES, and GP prediction models (the first scenario). Next, time series were denoised using the wavelet transform method, and then the prediction was made based on the denoised time series (the second scenario). To investigate the performance of the models in the first and second scenarios, nonlinear dynamic and statistical analysis, as well as chaos theory, was used. Finally, the analysis results of the second scenario were compared with those of the first scenario. The comparison revealed that denoising had a positive impact on the performance of all the models. However, it had the least influence on the GP model. In the time series produced by all the models, the error rate, embedding dimension needed to describe the attractors in dynamical systems and entropy decreased, and the correlation and autocorrelation increased. HIGHLIGHTS Conducting nonlinear dynamic and statistical analyses, as well as a chaotic analysis of the performance of the models.; Performing nonlinear dynamic and chaotic analyses of denoising influences on the performance of ARIMA, QES, GP, RBF, and ANN-MLP; Carrying out a statistical analysis of denoising impacts on the performance of forecasting models and comparing the results;

Keywords

• artificial neural network
• autoregressive integrated moving average
• chaos
• grid partitioning anfis
• quadratic exponential smoothing
• radial basis function