The Research On Vector Autoregressive Forecast Model With Penalty Functions

Prediction Theory and Methodology is an important research area in Management Science and Engineering,while the related research on regression prediction models has become a research focus in this field.In recent decades,the regression prediction models are widely used in other areas including industry and agriculture,economic management,education,psychology and medicine.In the initial regression models,we tend to add as many independent variables as possible to decrease the deviation of the model.However,with more and more data being collected,the dimension of the variables become higher and higher,so the explanation and accuracy of the prediction models are facing great challenges.For high-dimensional sparse data,a NP combinatorial optimization problem is often needed when it comes to regression model.When the dimension of the variables is large to a certain extent,we need to improve the traditional forecasting models and the corresponding solution algorithms as they are no longer applicable.High dimensional regression models often choose variable selection methods to reduce the com-plexity of the model,then it can improve the predication performance.A widely accepted approach is ordinary squares(OLS)estimations based on penalty functions.This predication model can be achieved by obtaining the estimated value of the parameters,in case of its penalty function reaches its minimum value through restricting some parameters in the model.A common feature of this model is that the selected variables are decided by the penalty functions.But in practical applications,there often exists multicollinearity between variables,leading to instability of estimations,and even the loss of some im-portant variables,thus the prediction is not accurate enough.The traditional methods including ridge regression,lasso regression and elastic net regression model hardly achieve desired results as they do not take prior distribution information of variables and correlations between variables into account.In order to improve the prediction accuracy,we propose a regularization punishment likelihood function method,taking correlations between variables and prior distribution information of variables into account to estimate the unknown variables and select useful variables.We also apply this approach to vector autoregressive prediction models.In this paper,the specific work is as follows:(1)In this paper,we propose a method based on the combination of the bridge punishment and Laplace regularization likelihood function to select variables.This method not only solves the multi-collinearity problems,but also deal with the variable selection problem of the sparse model,in which the number of variables is greater than samples.In order to establish the Laplacian graph matrix,we first consider the prior correlative information between variables,then construct the weighting function matrix based the scale free topology criterion and Pearson correlation coefficient.At the same time,we also combine the symbolic information between the interrelated variables and use the original data to cycle estimate the symbols coefficients.When solving the likelihood equation and seeking the estima-tion value of prediction variables,we present modified Newton-Raphson algorithm and cycle coordinate descent methods to select the useful variables and discard irrelevant variables from the results.Then,this paper presents some evaluation criteria.Based on this standard,we compare the proposed method with the other classical penalty function methods,such as Lasso regression,elastic net regression,weight fu-sion regression and network-constrained regularization regression.The experimental results show that the proposed method is better.(2)This article also discusses the compression characteristics of the bridge and graph regulariza-tion penalty function.In the bridge penalty function based regression model,conclusions about the compression are imperfect,so the present methods have no perfect results.We verify that the expression equations possess some compression characteristics,which provides evidence for selecting appropriate penalty functions in later examples.(3)We apply the proposed method to vector autoregressive model and use the correlation informa-tion of time series data to convert the vector autoregressive model into a linear regressive model.First,the unknown variable parameter matrix can be converted to a vector,then the variable selection prob-lem can be discussed in this framework.This idea is a kind of innovation.In addition,the simulation experiments and two real data are provided to validate the efficiency and reliability of the method and furthermore to compare its computational effectiveness with other classical penalized function methods.The experimental results show that the proposed method can well handle the variable selection problem in vector auto regressive model,and the method can get a better prediction.(4)This thesis gives some theoretical analysis and feasible verifications on presented penalized methods.In particular,we verify that the expression on estimation formulas follows Oracle property,in particular,the convergence properties.In Statistics,we prove that estimation formulas satisfy central limit theorem and grouping effect.As a result,the reasonable of the presented model is proved and the feasibility of the method is tested.(5)The proposed method is used to the prediction of several real examples.For three time series data of human gut microbiome data,we use the vector autoregressive model based on the combination of the Bridge punishment and network-constrained regularization to predict the microbial interactions.In particular,the correlation information between the bacteria is considered in this model.In the algorithm,based on the similarity of the original data,we first establish the weighted function matrix,and then use cyclic coordinate descent method to estimate the symbol variables.The results of the comparison experiment results show that the proposed method works better.In addition,we apply this method to paper data on biomedicine academic conference,then make a prediction and visualization on the relationship of interesting topics.