Chaotic Bayesian Method Based on Multiple Criteria Decision making (MCDM) for Forecasting Nonlinear Hydrological Time Series

To improve the precision and decrease the uncertainty in forecasting nonlinear hydrological time series, a novel chaotic Bayesian method based on multiple criteria decision making (CBMMCDM) is proposed, in which chaotic forecast model of the add-weighted one-rank local-region method (AOLM) is improved by embedding sell-learning technique of Bayesian processor of forecast (BPF) In addition, we give the optimal embedding dimension by use of MCDM theory for global parameter decision in CBMMCDM. So as to test the effect of CBMMCDM, the daily tuna's at Panjiakou and Sandaohezi in Luanhe basin are considered. The results of the phase-space reconstruction indicate that both of the above two daily runoffs ale chaotic series and their optimal embedding dimensions are both 3 with the low assessment indices of mean relative error (MIZE), root mean square error (RMSE), modified coefficient of efficiency (MCE) and Bayesian correlation score (BCS). Compared with the results of AOLM, CBMMCDM can improve the forecast accuracy of daily runoffs Especially relative errors also decrease in forecasting the maximum daily runoff values in both stations This new forecast method is an extension to chaos prediction method.