Testing Serial Correlation In Non-linear Model With Validation Data

People can only observe a small part of the exact value of the variable when observing the target variable,and we call the small fraction of the data that can be accurately observed as the verify data.In statistical simulation,the error of the ideal fitting model is generally considered to be independent identically distributed(i.i.d.).So when we fit the data and get the fitting model,we have another job of checking whether the error sequences of the model are independent of each other.This paper considers the sequence correlation test of nonlinear model with verification data.Firstly,the function of the established verification data and primary data are transformed into a conventional nonlinear model.Second,the unknown parameters are estimated by the least square method,and obtain the test statistic by empirical likelihood method.Then,the lemma 3.2 and lemma 3.3 are proved.Through the given conditions C and lemma 3.1-lemma 3.5,we establish the nonparametric Wilk's s theorem for testing sequence correlation,that is theorem 3.1.Finally,we designed four test models.The explain variable and the response variable are quadratic function or exponential function.The verification data and the main data are linear function or sine function.The error sequence of the model will have first order and two order correlation.Simulation results show that,irrespective of the model under which the error obeys,the size is close to the given level of significance 0.05 under the null hypothesis;Under the alternative hypothesis,with the increase of the error sequence correlation,the increase of the sample size and the increase of the sample size,the level and efficiency of the test are better and better.