In this paper,we focus on the BDS test,which is a nonparametric test of independence.Specifically,the null hypothesis H0 of it is that {u_(t)} is i.i.d.(independent and identically distributed),where {u_(t)} is a rand...In this paper,we focus on the BDS test,which is a nonparametric test of independence.Specifically,the null hypothesis H0 of it is that {u_(t)} is i.i.d.(independent and identically distributed),where {u_(t)} is a random sequence.The BDS test is widely used in economics and finance,but it has a weakness that cannot be ignored:over-rejecting H0 even if the length T of {u_(t)} is as large as(100;2000).To improve the over-rejection problem of BDS test,considering that the correlation integral is the foundation of this test,we not only accurately describe the expectation of the correlation integral under H_(0),but also calculate all terms of the asymptotic variance of the correlation integral whose order is O(T^(-1))and O(T^(-2)),which is essential to improve the finite sample performance of BDS test.Based on this,we propose a revised BDS(RBDS)test and prove its asymptotic normality under H0.The RBDS test not only inherits all the advantages of BDS test,but also effectively corrects the over-rejection problem of it,which can be fully confirmed by the simulation results we presented.Moreover,based on the simulation results,we find that similar to BDS test,RBDS test would also be affected by the parameter estimations of the ARCH-type model,resulting in size distortion,but this phenomenon can be alleviated by the logarithmic transformation preprocessing of the estimate residuals of the model.Besides,through some actual datasets that have been demonstrated to fit well with ARCH-type models,we also compared the performance of BDS test and RBDS test in evaluating the goodness-of-fit of the model in empirical problem,and the results reflect that,under the same condition,the performance of the RBDS test is more encouraging.展开更多
基金the National Natural Science Foundation of China(12271536,12171198)First Class Discipline of Zhejiang-A(Zhejiang University of Finance and Economics-Statistics)(10344921011/003).
文摘In this paper,we focus on the BDS test,which is a nonparametric test of independence.Specifically,the null hypothesis H0 of it is that {u_(t)} is i.i.d.(independent and identically distributed),where {u_(t)} is a random sequence.The BDS test is widely used in economics and finance,but it has a weakness that cannot be ignored:over-rejecting H0 even if the length T of {u_(t)} is as large as(100;2000).To improve the over-rejection problem of BDS test,considering that the correlation integral is the foundation of this test,we not only accurately describe the expectation of the correlation integral under H_(0),but also calculate all terms of the asymptotic variance of the correlation integral whose order is O(T^(-1))and O(T^(-2)),which is essential to improve the finite sample performance of BDS test.Based on this,we propose a revised BDS(RBDS)test and prove its asymptotic normality under H0.The RBDS test not only inherits all the advantages of BDS test,but also effectively corrects the over-rejection problem of it,which can be fully confirmed by the simulation results we presented.Moreover,based on the simulation results,we find that similar to BDS test,RBDS test would also be affected by the parameter estimations of the ARCH-type model,resulting in size distortion,but this phenomenon can be alleviated by the logarithmic transformation preprocessing of the estimate residuals of the model.Besides,through some actual datasets that have been demonstrated to fit well with ARCH-type models,we also compared the performance of BDS test and RBDS test in evaluating the goodness-of-fit of the model in empirical problem,and the results reflect that,under the same condition,the performance of the RBDS test is more encouraging.
