Short-term Forecast Of China's Economy Based On Fractional Order Mode

The outbreak of the novel coronavirus has had a profound impact on China’s economic activities,and it is one of the important research issues in the process of economic recovery to timely determine the main influencing factors of the epidemic on economic growth and forecast the future economic trend.Fractional derivative can be used to describe the dynamic behavior of nonlinear,non-local and non-stationary systems.It has the characteristics of memory and heredity,and can describe the dynamic evolution process of complex economic systems more accurately.In this paper,the classical Caputo fractional derivative is used to establish a fractional economic model to forecast and analyze the quarterly Gross Domestic Product(GDP)after the epidemic,and on this basis,the influence of fractional derivative of different kernel functions on economic forecast is explored.The application scope of fractional derivative in economic forecasting is extended.The main research contents of this paper are as follows:(1)Forecasting and analysis of quarterly GDP using Caputo fractional order derivatives.Firstly,an improved economic forecasting index system is constructed,and an economic forecasting model(GA-Caputo)is established by combining Genetic Algorithm(GA)and Caputo fractional derivative,and the model parameters are calculated.Secondly,seasonal ARIMA(differential autoregressive moving average)model and BP(Back propagation)neural network are selected for comparison.Finally,the fitting and forecasting results show that the GA-Caputo model has good fitting performance and forecasting effect on the short-term economic growth trend under the epidemic situation,and the average absolute percentage error is 10.86 and 0.74 percentage points lower than that of seasonal ARIMA and BP neural network,respectively.In addition,the relative error of the GA-Caputo model is smaller at multiple prediction set time points,which indicates that the GA-Caputo model has better robustness.(2)Comparative analysis of variable kernel fractional order economic models.First,in view of the nonlinearity,random volatility and periodicity of the data in this paper,the kernel function is changed to introduce different fractional derivatives(Hadamard,Erdely-Kober,Weyl)to establish a fractional economic model,so as to verify the merits and demerits of the fractional derivatives of different kernel functions for the modeling of the problem in this paper.Secondly,the kernel function form of Caputo fractional derivative and Hadamard fractional derivative obtained under fixed order is suitable to describe the economic growth trend under the epidemic.The results show that GA-Hadamard model has the best fitting performance and forecasting effect,and the average absolute percentage error is 4.45,3.93 and 0.27 percentage points lower than GA-EK,GA-Weyl and GA-Caputo models,respectively.Finally,it is concluded that when the order of economic variables of GA-Hadamard model is between 0.5 and 1,it can respond quickly to economic fluctuations under the epidemic and has a greater impact on quarterly GDP.The selected variables are as follows: To put forward corresponding policy suggestions on the total export value,total retail sales of consumer goods,fiscal revenue and industrial added value,as a reference for post-epidemic economic recovery.