Multi-scale Combined Forecasting Methods And Their Applications Based On Times Series Characteristic Driven Decomposition

Time series forecasting has significant theoretical research and practical background,which has been widely applied to the forecasting fields of economics,finance,energy and environment,etc.With the increasing complexity of social systems,the time series of forecasting indicators are often nonlinear and non-stationary.Due to the superiority of decomposition-ensemble forecasting model in dealing with non-stationary and nonlinear time series forecasting,it has gradually become one of the important tools for time series forecasting.Because individual forecasting methods of different time series have their own characteristics;it is of great theoretical and application value to explore the multi-scale combined forecasting methods and properties based on time series characteristic driven decomposition.There are still some theoretical and application problems worth further research by the systematic study of the literature based on decomposition-ensemble forecasting models.Firstly,the existing decomposition-ensemble forecasting models usually use the individual forecasting models to forecast the decomposed series and the forecasting results of the decomposed series directly affect the results of multi-scale forecasting results.The individual forecasting models may bring large errors and increase the risk of forecasting.Secondly,the numbers of time series obtained by decomposition approaches are generally large in decomposition-ensemble forecasting models.If the models are constructed for all series,the calculation of the model is too large,and it may lead to the cumulative effect of errors.Thirdly,for the interval-valued multi-scale forecasting models,there is no literature discussing the construction of combined forecasting model for the decomposed series.Moreover,the existing models usually only consider the forecasting error of the endpoint of the interval-valued and ignore the length error of the interval,which will lead to an increase in the uncertainty of the forecasting results.Fourthly,the existing multi-scale forecasting models only consider the influence of historical data.In fact,the forecasting results may be affected by other external influence factors and some unstructured data.In view of the above problems,this dissertation aims to propose several kinds of multi-scale combined forecasting models based on time series characteristic driven decomposition and apply them to actual forecasting problems.The main studies are as follows:(1)Aiming at the existing multi-scale forecasting model based on ensemble empirical mode decomposition(EEMD),in order to deal with the end effect which occurs during the sifting process,and only utilize individual forecasting models to forecast the decomposed series,the multi-scale combined forecasting model based on improved EEMD is proposed.On the basis of the original time series processed by the mirror method,the processed series is decomposed by the EEMD method.Then,different individual forecasting models are employed to forecast the obtained series and a multi-scale combined forecasting model is developed based on L1 norm with EEMD method.The superior properties of the proposed model are studied.Considering that forecasting accuracy varies with methods and time points,the varied weight multi-scale combined forecasting model is constructed based on improved EEMD method.An empirical analysis of air quality index forecasting results of error index,validity index and DM test indicate the effectiveness of the methods.(2)For the problem of obtaining a large number of sequences after time series decomposition,by studying the characteristics of the series,it is found that some of the time series are of similar importance to the forecasting of the original time series in terms of trend accuracy and relative error.Hence,the comprehensive contribution index(CCI)of each series to original time series is constructed and series are further reconstructed by evolutionary clustering algorithm according to CCI.Then,the multi-scale combined forecasting models based on decomposition approaches(i.e.variational mode decomposition(VMD)and EEMD)with evolutionary clustering are constructed,respectively.The properties of the proposed models are studied and the two models are applied to the forecasting of crude oil price and carbon price with high volatility.The empirical results in different fields illustrate the rationality of the proposed methods.(3)For the interval-valued multi-scale forecasting model,this dissertation follows the research idea from simple to complex.Firstly,the upper and lower bounds of interval-valued time series are regarded as two independent series,and decomposed by EEMD method,respectively.Then,a simple and effective interval-valued multi-scale combined forecasting model is constructed based on EEMD approach.Secondly,considering that the correlation of the upper and lower bound is ignored when the endpoints of the interval value time series are predicted separately.This dissertation uses the efficient bivariate empirical mode decomposition(BEMD)method for the complex-valued series decomposition,and the upper and lower bounds are decomposed at the same time.The different interval-valued individual forecasting methods are utilized to forecast the decomposed interval series.Then,the interval-valued multi-scale combined forecasting model based on BEMD method is proposed and the properties of the model are studied.Thirdly,considering that the existing interval-valued multi-scale forecasting models only focus on the forecasting error of the endpoints,in order to deal with the problem,the interval values are expressed in terms of upper and lower bounds as the midpoints and radius,then the multi-objective combined forecasting model based on decomposition of midpoints and radius by BEMD method is proposed.Through the analysis of interval-valued time series,the air quality index forecasting in Hefei illustrates the rationality of the three interval-valued multi-scale combined forecasting models(4)The existing decomposition-ensemble forecasting models mostly consider historical data and ignore the influence of other external factors and some unstructured data.This dissertation considers the comprehensiveness of data information and selects suitable forecasting models according to different data sources,and then a novel combined forecasting model with multi-source information is developed.From perspective of cooperative games,an improved Shapley value is proposed to determine weights of combined forecasting model.In order to further enhance the forecasting accuracy,a combined forecasting model with multi-source information based on Lp norm is constructed.The special cases are discussed when the parameter p takes different values,meanwhile the whale algorithm is utilized to optimize the parameter p.By utilizing a numerical study of the carbon price data from Shenzhen,the results confirm that the proposed approach outperforms benchmark models in terms of some statistical measures and robustness.