Nonparametric Robust Estimation Of Functional Coefficient Cointegration Model And Its Application

In the development of economic time series analysis,models based on conditional expected mean play an important role.Most models derive current and even future trends through stable historical relations between variables.It is generally required that data be controllable and recursible,that is,to satisfy stationarity,which also forms the cornerstone of classical econometrics.With the deepening of economic research,it is found that most time series show nonstationary characteristics.If the characteristics are not properly identified,the distortion of traditional test statistics may occur during regression analysis,and then spurious regression will be generated.Since Engle and Granger proposed the Cointegration Theory,the research field extends to the linear model between non-stationary sequences.However,the current political and economic environment at home and abroad makes the relationship between economic variables show abnormal complexity.and the equilibrium relationship between nonstationary data is difficult to keep the linear constant in the long term.Large deviations may occur when traditional models are used to capture the Cointegration relationship.At this point,Nonparametric and Semiparametric modeling requires less prior information on model structure,avoids the possible model misspecification to a certain extent,and discover the intrinsic relationship of data more accurately.Nonparametric modeling process of Cointegration theory involves kinds of key factors,such as local estimation method,bandwidth selection and residual-based stationarity test,which have a decisive influence on analysis result.The proper use of the method requires expertise and experience.In view of the "Curse of Dimensionality" of nonparametric modeling,the Functional Coefficient Models developed later is often applied to the study of complex economic problems.Most of the discussion about model estimation,specification test and asymptotic properties is based on strict assumptions of homoscedasticity and normality.Ignoring the possible heteroscedasticity and heavy-tailed features of the sequence may lead to model misspecification,test statistics distortion,or uneffective estimators.In order to solve the above problems and improve the Cointegration theory’s ability to explain practical problems,the main research contents are as follows.Firstly,the nonparametric modeling and identification of complex Cointegration relationship from the perspective of combinatorial method was proposed.Considering the local estimation method,bandwidth selection method and residual-based stationarity test in the whole process of nonparametric modeling,the optimal residual sequence was extracted and the cointegration relationship was effectively verified.Secondly,Focusing on the Functional Coefficient Cointegration Model(FCCM)with flexibility and dynamics,a nonparametric estimation method taking into account the possible time-varying volatility was proposed.Furthermore,considering the heavy-tailed and different kinds of heteroscedasticity features of the data,a robust nonparametric estimation method suitable for the features was found.Finally,In order to further reflect the practical significance of the research,the proposed modeling and robust estimation methods proposed above were applied to retest the Purchasing Power Parity theory between China and the world’s major economies,and valuable conclusions were obtained after comparative analysis with traditional models and estimation methods.The study found that:Firstly,the Combinatorial method consisting of Local Linear estimator,Cross Validation method,plus Variance Ratio test has good Size properties in recognition of real cointegration relationship,and the ADF test has good Power properties on the identification of spurious one.The method still has good properties when the Moderate Deviation Unit Root Sequence considered.Secondly,the Kernel Weight Least Square estimator of FCCM becomes a uneffictive estimator due to the influence of asymptotic variance when time-varying volatility is included in the data.The adaptive method can effectively identify the possible time-varying volatility,and the local linear kernel estimation can improve the estimation of the boundary.Finally the improved Local Linear Adaptive KLS estimation performs better in coefficient estimation accuracy,overall model fitting,and identification of cointegration relations.Thirdly,a feasible local linear Adaptive Least Absolute Deviations Estimator(ALADE)is proposed when the models with heavy-tailed features and different kinds of heteroscedasticity.The performance of the Cross Validation method and Absolute value Cross Validation method was creatively analyzed and the advantage of the latter in selecting the optimal bandwith is verified.The new method yield more accurate coefficient estimation and overall model fitting,and perform better on optimal bandwidth selection and identification of cointegration relations.Finally,the validity of Purchasing Power Parity theory between China and Russia is verified by nonparametric combinatorial method,and the FCCM is constructed and the theory between China and Britain is verified by feasible local linear ALADE method.The robustness of the proposed nonparametric estimation methods are verified by real data,which makes up for the limitation of simulated sample generation to a certain extent.The innovative works of this paper are as follows:Firstly,a nonparametric combinatorial method is proposed to model and identify complex Cointegration relations,which solves the problem of method selection of key factors in the process.Meanwhile,the Size and Power performance of the combinatorial method with moderate deviation from the unit root process are studied expansively.It provides an efficient and operational estimation process for all researchers.Secondly,focusing on the Functional Coefficient Model,the local linear Adaptive Kernel Weighted Least Squares estimation is proposed.This method can provide robust estimation results for time series with time-varying volatility characteristics.Thirdly,considering the heavy-tailed characteristics and heteroscedasticity in time series,a feasible local linear Adaptive Least Absolute Deviations Estimator is proposed,and the superiority of absolute value cross validation method in selecting bandwith is verified.The ability of the cointegration theory to analyze real problems is improved and its application scenarios are extended.Finally,the innovative modeling and estimation methods are re-examined for the economic problems between China and the world’s major economies,and valuable conclusions are obtained after comparative analysis with traditional models and estimation methods.