Research On Multicollinearity And Autocorrelation In GM(1,N) Model

Multiple collinearity and autocorrelation are two common morbidities in traditional statistics.They can make the model very unstable and get erroneous results.The grey GM(1,N)model may also have multiple collinearity and autocorrelation due to accumulated processes and lagged terms.Studying the morbidity of GM(1,N)model caused by multiple collinearity and autocorrelation among variables has important practical significance for improving the prediction accuracy of GM(1,N)model.First,the multiple collinearity in the GM(1,N)model is studied.In order to diagnose the multiple collinearity in the GM(1,N)model,for the GM(1,N)model's little information characteristics,the grey relational degree is used to measure the linear correlation among multiple variables,and the eigenvalue method is used to diagnose the degree of multicollinearity.In order to deal with the problem of multiple collinearity in the GM(1,N)model,the principal component-ridge regression method is introduced into the GM(1,N)model.The admissibility and superiority of the principal component-ridge regression method are mainly studied.It is proved that the principal component-ridge regression method is an admissible estimation in the linear estimation class under the equilibrium loss,and is better than the least-square estimation,principal component regression and the ridge estimation under the equilibrium loss function.Second,the autocorrelation in the GM(1,N)model is studied.To diagnose various types of autocorrelation in the GM(1,N)model,a graphic method is used to diagnose the positive and negative autocorrelations in the GM(1,N)model,using the Lagrange multiplier of the GM(1,N)model to diagnose the degree of autocorrelation in GM(1,N)Model.In order to deal with the autocorrelation problem in the GM(1,N)model,the generalized difference method of the GM(1,N)model is introduced.The autocorrelation coefficient is estimated by combining the regression test and the Cochrane-Aocott iteration method.Finally,an empirical analysis of the multiple collinearity and autocorrelation problems in the GM(1,N)model based on the original data of the economic growth indicators of Hubei Province is conducted.Firstly,the GM(1,8)model was established by using Hubei Province's GDP and its main influencing factors as variables,and ridge estimation and principal component-ridge regression methods are used.By comparison,the principal component-ridgeregression method has overcome the multiple collinearity in the GM(1,8)model and is superior to the LS estimation and ridge estimation.After detecting the second-order autocorrelation in the model,the generalized difference method and the Cochran-Ocot iteration method are combined,and satisfactory results are obtained after four iterations.By comparison,the generalized difference method of the GM(1,8)model overcomes the problem of autocorrelation.