Extended Research Of Grey Prediction Model With Time-delay Effect And Its Application

For the problem of prediction model of small sample data series with time-delay effect,the existing model usually assumes that the time-delay period is a fixed value,ignoring the influence of the dynamic change of time-delay value on the prediction effect of the model.In order to overcome this limitation,starting from the dynamic characteristics of system time-delay effect and assuming that the system time delay is a function of time,a GM(1,1|?i)model with time-varying delay function and a strong compatibility DGM(1,N,?i)model with time-delay function are constructed.Finally,aiming at the forecasting problem of the tourism development planning in China,we use the forecasting model designed in this paper to predict the number of inbound tourists and tourism revenue in China's tourism industry,and verify the validity and practicability of the gray prediction model with time-delay effect.The content includes the following aspects:(1)For the existing grey forecasting model with time-delay effect,it is usually assumed that the time delay is a fixed value.It is proposed that the dynamic effect of the system time delay should be considered in the model,and the static time-delay parameter of the GM(1,1|?,r)model is generalized as a time-varying delay function.The expressions of non-integer delays under different time-delay parameters are designed.The grey relational degree is used as the theoretical basis for parameter optimization of time-varying delay functions.Then according to the value of time-delay function,the parameter estimation and time response function of GM(1,1|?i)model are deduced.Finally,the model was applied to the prediction of port cargo throughput,and the prediction results of GM(1,1|?i)were compared with GM(1,1)and GM(1,1|?)models and analyzed to verify the validity of the model.(2)For the multivariable grey prediction model with time-delay effect,the dynamic effects of time-delay and multivariable time-delay variation are neglected in the model,and the time-varying delay is extended to the multivariable grey prediction model.Firstly,the static time-delay parameter is generalized as a generalized mathematical function,and corresponding time-delay parameter determination steps are designed according to whether the mathematical function is related to time.Then,the cumulative effect of time-delay and the correction of time-lag accumulation effect are considered in the model,and the parameter expression and time response function of the DGM(1,N,?i)model are obtained.Secondly,the compatibility of DGM(1,N,?i)model to DGM(1,N)?DDGM(1,N)and DDGMD(1,N)models is analyzed.Finally,the DGM(1,N,?i)model was applied to predict agricultural output value,and the prediction results of DGM(1,N,?i)was compared with the other three models to verify the feasibility and practicality of the model.(3)Applying the GM(1,1|?i)and DGM(1,N,?i)models designed in this paper to the forecast of tourism development planning in China.Firstly,the GM(1,1|?i)model was used to model the number of inbound tourists in China from January to December in 2014.The fitting results of the GM(1,1|?i)model verified the validity of the model,and analyzed the trend of the number of foreign tourists in China.Secondly,considering the impact of the number of tourists and tourism staff training on the tourism revenue in China,we use the DGM(1,N,?i)model to forecast China's tourism revenue.Finally,analyzing the main driving factors that affect China's tourism revenue and its impact on forecasting.