Empirical Likelihood Method For GARCH-M Models

This paper deals with the metric of risk aversion, and test statistics of GARCH-M model are constructed by the empirical likelihood method. Under mild conditions,for regular GARCH-M model, asymptotic chi-square distributions of test statistics areobtained. And then the confidence interval of the beta is also obtained through profilelikelihood. Simulations show that the empirical likelihood method behaves well.To begin with, in the exordium, we introduce the concepts of individual riskaversion and the situations of empirical likelihood’s development.Chapter2introduces the classic ARCH model, and gives the process of the tra-ditional empirical likelihood.The subsequent chapter3illustrates the GARCH-M model and discusses theprocess of the empirical likelihood. And we also implement the empirical likelihoodtheorem of the GARCH-M model. Then we get the confidence interval of the betathrough profile likelihood.Chapter4presents some simulations for the proposed model with the method ofempirical likelihood. And the results of the coverage rate perform well.Chapter5offers the detailed proof of the proposed theorems.