Interval-valued Linear Regression And Autoregressive Time Series Model With Constraints

In many fields,such as economy,finance,meteorology and so on,we often need to deal with interval data.In the past people often use the single in the interval values instead of interval value to analyse,it will lose a lot of information.In this paper,the interval value is used as a whole data.The main research is the interval valued linear regression model with constraints and the interval autoregressive time series model with constraints.Firstly,we introduce the basic concepts of set valued random variables and its expectation,variance and so on.Then the existing interval value regression models are summarized,and the advantages and disadvantages of each model are analyzed.According to the previous model,the problem that the left end of the interval is sometimes greater than the right endpoint in the prediction model.For this reason,we establish a new interval valued linear regression model with constraints.In this model,the expectation of the error term is not equal to zero due to the existence of the constraint condition,and it will have systematic deviation if we estimated the coefficients by the least squares estimation method.Therefore,we propose a two step estimation method.First step we produce an intermediate variable make the expectation of the error term zero under the constraint condition to establish a new model,and then to estimate the parameters of the new model with the least squares of the interval d2 value in the second step.This method mainly combines maximum likelihood estimation with the least squares estimation method.Based on the interval valued linear regression model with constraints,we study the interval autoregressive time series model with constraints,and also use the two step estimation method to solve the problem of the system deviation about the parameter estimation.On the basis of the established model and method,we compare the results with the least squares estimation by Monte Carlo simulation,and proved the validity of the two step estimation method.And then three evaluation standard model are adopted to compare the establish model with the existing models respectively,and the superiority of the model is further illustrated.Finally,a practical example is used to illustrate the practicality of the model and method.