Research And Application Of Fractional Cointegration Test For A Class Of Error Correction Models

Co-integration theory has been equipped with a complete system of modeling theories and methods since its establishment.It is gradually becoming an important tool for studying non-stationary time series in the modern financial field.However,in the case of long memory series,long-term equilibrium relationships cannot be correctly characterized by cointegrating co-integration relationships.Existing studies have shown that it is more reasonable to study fractal co-integration under the fractal framework.Among them,the thinking and exploration of the hypothetical distribution conditions of the fractional co-integration model need to be further deepened.Under the fractal framework,this paper focuses on the modeling of fractional co-integration,improves the fractional co-integration test from different hypothetical distributions of the model,and proposes a new fractional co-integration test algorithm.First,on the basis of reviewing the theory of fractional co-integration,the selection and setting of fractional linear co-integration models are discussed and analyzed.Previous studies have shown that error correction models(ECM)based on single integers cannot describe long-memory scores.The cointegration relationship between integer sequences.This article uses a fractional vector error correction model(FVECM)that can correctly model fractional and integer sequences with the same or different fractional integrals.Under the setting of the FVECM model,two fractional cointegration integrations are given.This kind of definition constructs a test equation based on least squares(OLS)regression,adopts the robust KPSS test and F test under fractional integral,and discusses the progressive distribution of test statistics.Secondly,in order to break through the limitation that the residuals of the FVECM model obey independent and identical distributions,this paper proposes two improved fractional co-integration testing methods for sequence heteroscedasticity and non-linear sequence dependent distribution.The Wild bootstrap(WB)algorithm is used to reconstruct the resampling residual items to construct a WB-based fractional co-integration test for sequence heteroscedasticity.The Autoregrees wild bootstrap(AWB)algorithm was introduced.By deriving the principle of multiple invariance of the AWB algorithm,the simultaneous capture of heteroscedasticity was analyzed.Based on the theoretical basis of data dependence and sequence dependence,a full data-driven AWB score co-integration test is proposed.Monte Carlo simulation results show that the improved algorithm has good finite sample properties under heteroscedasticity and sequence dependence,and bootstrap co-integration test methods based on threshold methods have lower test level distortion.Finally,empirical research on silver futures positions based on two improved fractal co-integration methods of WB and AWB.The empirical results show that COT Silver Futures positions have significant long memory,heteroscedasticity and non-linear sequence dependence.There is a fractional cointegration relationship between the sequence of commercial and non-commercial positions.