Kink Model Averaging Based On AMMA Criterion

Model averaging is a statistical method that incorporates model uncertainty into the modeling process and uses weighted averaging of statistical inferences from different models to make final inferences.It is a hot topic in statistics and econometrics research,and is widely used in various fields such as economics,finance,and meteorology.For example,in the process of modeling and forecasting,because the model averaging method is not based on a single model for forecasting,but rather uses the weighted average of the predicted values of multiple models for forecasting,which can largely avoid the problem of poor forecasting results caused by the selection of a single model.How to estimate the weighted weights is one of the most important issues in the research of model averaging methods.The Mallows Model Averaging(MMA)method proposed by Hansen(2007)is the most commonly used weight estimation method,with the basic idea of selecting weights by minimizing the Mallows criterion.Due to the assumption that candidate models are strictly nested in the MMA method,it is difficult for the MMA method to estimate the optimal weight when the largest candidate model is not unique or does not exist.The adjusted Mallows Model Averaging(AMMA)criterion has a wider application because it does not need to assume the existence and uniqueness of the maximum model.Kink regression model(or continuous threshold model)is a threshold regression model with constraints that have inflection points at unknown thresholds and are continuous everywhere.It is widely used in many fields such as economics.This paper studies the averaging problem of the kink regression model based on the AMMA criterion.The main contents are as follows:(1)Under the condition that the threshold value of the kink regression model is regarded as a normal model parameter,the AMMA criterion is applied to the average of the kink model.Firstly,the parameters of the kink model are estimated using the least square method,and then an adjusted Mallows criterion is constructed based on the model fitting residuals.Finally,the optimal weight of the candidate model is estimated by optimizing the adjusted Mallows criterion,and the asymptotic optimality of the obtained weights is theoretically proved.The results of numerical simulation and empirical analysis of a group of US GDP data indicate that,compared to the methods already available in literature such as MMA,when making predictions based on the optimal weights obtained by the AMMA criterion proposed in this chapter,in most cases,there is relatively small prediction error,especially when the existing model averaging method is not applicable,the AMMA criterion has significant advantages.(2)In order to avoid estimating threshold parameters in kink regression models,kink regression models with different threshold values are considered as different candidate models,and the AMMA criterion is further used to study the averaging problem of kink regression models.The theoretical proof results show that the weights obtained at this time still satisfy the asymptotic optimality,and the numerical simulation results show that compared to the case where the threshold parameter values are estimated first and then averaged by the model,due to the model averaging of more candidate models at this time,there is relatively smaller prediction error in most cases.Finally,the practicability of the proposed method is illustrated by analyzing a set of Chinese CPI index data.