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
Unlike the Brock,Dechert,and Scheinkman(BDS)test,the Surrogate Data method is not only able to provide a nonlinearity test for exchange rates,but also distinguish whether the nonlinear features come from the economic ...Unlike the Brock,Dechert,and Scheinkman(BDS)test,the Surrogate Data method is not only able to provide a nonlinearity test for exchange rates,but also distinguish whether the nonlinear features come from the economic system itself.Our analysis gives some evidence on the presence of nonlinear dependency of five emerging markets' exchange rates by using BDS test.Furthermore,we present evidence in existence of intrinsic and deterministic nonlinearity in the five exchange rates using the Surrogate Data method,comparing the original data and surrogate data and rejecting the null hypothesis in confidence coefficient 95%.The results provide the basis for the analyses of the chaotic properties of exchange rate time series and their future nonlinear forecasting.展开更多
Tensile strength is an important material property for rocks. In applications where rocks are subjected to dynamic loads, the dynamic tensile strength is the controlling parameter. Similar to the study of static tensi...Tensile strength is an important material property for rocks. In applications where rocks are subjected to dynamic loads, the dynamic tensile strength is the controlling parameter. Similar to the study of static tensile strength, there are various methods proposed to measure the dynamic tensile strength of rocks.Here we examine dynamic tensile strength values of Laurentian granite(LG) measured from three methods: dynamic direct tension, dynamic Brazilian disc(BD) test, and dynamic semi-circular bending(SCB). We found that the dynamic tensile strength from direct tension has the lowest value, and the dynamic SCB gives the highest strength at a given loading rate. Because the dynamic direct tension measures the intrinsic rock tensile strength, it is thus necessary to reconcile the differences in strength values between the direct tension and the other two methods. We attribute the difference between the dynamic BD results and the direct tension results to the overload and internal friction in BD tests. The difference between the dynamic SCB results and the direct tension results can be understood by invoking the non-local failure theory. It is shown that, after appropriate corrections, the dynamic tensile strengths from the two other tests can be reduced to those from direct tension.展开更多
This paper presents some empirical evidences on the presence of nonlinearity of exchange rates of six emerging markets by using Brock-Dechert-Scheinkman(BDS)test and Volterra-Wiener-Korenberg(VWK)model,respectively.Th...This paper presents some empirical evidences on the presence of nonlinearity of exchange rates of six emerging markets by using Brock-Dechert-Scheinkman(BDS)test and Volterra-Wiener-Korenberg(VWK)model,respectively.The nonlinear dependences are found in the exchange rates of six emerging markets.Furthermore,this paper applies the VWK model with surrogate data method to detect if their nonlinear dependences are deterministic or not.The results show that the above exchange rates are deterministic and nonlinear time series.These imply that the exchange rate markets do not conform to the requirements of the random walk hypothesis.Therefore,the nonlinear dynamic model should be used to analyze the exchange rates.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.
文摘Unlike the Brock,Dechert,and Scheinkman(BDS)test,the Surrogate Data method is not only able to provide a nonlinearity test for exchange rates,but also distinguish whether the nonlinear features come from the economic system itself.Our analysis gives some evidence on the presence of nonlinear dependency of five emerging markets' exchange rates by using BDS test.Furthermore,we present evidence in existence of intrinsic and deterministic nonlinearity in the five exchange rates using the Surrogate Data method,comparing the original data and surrogate data and rejecting the null hypothesis in confidence coefficient 95%.The results provide the basis for the analyses of the chaotic properties of exchange rate time series and their future nonlinear forecasting.
基金provided by the Innovative Research Groups of Natural Science Foundation of China (NSFC) (Grant No. 51321065)NSFC (Grant No. 51479131)The research of Kaiwen Xia was partially supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) through the Discovery (Grant No. 72031326)
文摘Tensile strength is an important material property for rocks. In applications where rocks are subjected to dynamic loads, the dynamic tensile strength is the controlling parameter. Similar to the study of static tensile strength, there are various methods proposed to measure the dynamic tensile strength of rocks.Here we examine dynamic tensile strength values of Laurentian granite(LG) measured from three methods: dynamic direct tension, dynamic Brazilian disc(BD) test, and dynamic semi-circular bending(SCB). We found that the dynamic tensile strength from direct tension has the lowest value, and the dynamic SCB gives the highest strength at a given loading rate. Because the dynamic direct tension measures the intrinsic rock tensile strength, it is thus necessary to reconcile the differences in strength values between the direct tension and the other two methods. We attribute the difference between the dynamic BD results and the direct tension results to the overload and internal friction in BD tests. The difference between the dynamic SCB results and the direct tension results can be understood by invoking the non-local failure theory. It is shown that, after appropriate corrections, the dynamic tensile strengths from the two other tests can be reduced to those from direct tension.
基金the Key Projects of the China National Fund for Social Science(No.09AJY003)the Humanities and Social Sciences Project of Ministry of Education(No.2009JYJR037)
文摘This paper presents some empirical evidences on the presence of nonlinearity of exchange rates of six emerging markets by using Brock-Dechert-Scheinkman(BDS)test and Volterra-Wiener-Korenberg(VWK)model,respectively.The nonlinear dependences are found in the exchange rates of six emerging markets.Furthermore,this paper applies the VWK model with surrogate data method to detect if their nonlinear dependences are deterministic or not.The results show that the above exchange rates are deterministic and nonlinear time series.These imply that the exchange rate markets do not conform to the requirements of the random walk hypothesis.Therefore,the nonlinear dynamic model should be used to analyze the exchange rates.
