Jackknife Empirical Likelihood Ratio Test And Empirical Analysis For Serial Correlation

Many existing inference methods and their asymptotic distribution of time series model mainly depend on the following four preconditions:(1)the stationarity of the covariate series;(2)the structure of the correlation relationship of error series;(3)whether the variance of the error term is finite;(4)whether the intercept term of model is available.Different preconditions,the time series model and its asymptotic distribution will also be different,in which the structure of the serial correlation affects the validity of the parameter estimation.Therefore,serial correlation test is a very important concept in econometrics.As an essential basic assumption in statistical inference,such as parameter estimation and hypothesis test,it plays an important role in economic and financial fields.With the rapid development of China's economy,the government,investors and enterprises pay more and more attention to the dynamics of the stock market.The research on the predictability of the stock market has always been a hot issue in the fields of economy and finance.The prediction results of many economic and financial indicators are an important reference basis for financial activities such as formulating national macroeconomic policies and allocating fiscal funds.The predictive regression model in the time series model is often used to deal with the problem of predictability in economic and financial fields.At present,most of the researches on hypothesis testing and statistical inference based on the predictive regression model assume that there is no autocorrelation between error series.If there is a correlation between error serial,then the hypothesis testing and statistical inference based on this are invalid.Therefore,it is of great significance to test the serial correlation of predictive regression model in statistical inference.Therefore,this paper studies the correlation of error serial for the prediction regression model.Based on the empirical likelihood method,considering the calculation difficulties caused by the empirical likelihood method when the parameter dimension is too high,this paper combines the Jackknife method in non-parametric statistics to construct the Jackknife empirical likelihood ratio statistics.The asymptotic distribution of the test statistic is proved,and the corresponding random numerical simulation is performed to test the finite sample properties of the statistic,and it is compared with the general empirical likelihood method.The simulation results show that the proposed method has the advantage of testing in most cases.Finally,this paper uses the data of foreign stocks in the CRSP database and the related data of China Securities 500 index in order to verify the effectiveness of the method proposed in this paper.By combining the empirical likelihood method and the Jackknife method in nonparametric statistics,the Jackknife empirical likelihood ratio statistic is constructed to test the serial correlation of error terms,which not only opens up a new research ideas for the serial correlation testing.At the same time,the validity of statistical inferences such as parameter estimation and hypothesis testing based on the predictive regression models is guaranteed.The test method proposed in this paper is not only applicable to first-order serial correlation,but also to high-order serial correlation.To sum up,the series correlation test based on the predictive regression model has not only theoretical significance,but also practical significance.The specific chapters are as follows:The first chapter is the introduction.Firstly,it describes the research background and significance of this paper,and then combs the research status of the predictive regression model at home and abroad,and then expounds the main content of this paper——serial correlation test,to show the feasibility and significance of this research.Secondly,the research ideas and research framework of this paper are described,and finally,the innovation points of this paper and the difficulties existing in the research process are summarized.The second chapter is the theoretical basis,which respectively expounds the theoretical knowledge of empirical likelihood method and Jackknife empirical likelihood method,and simply expounds the relevant theoretical knowledge involved,so as to pave the way for the reasoning proof in the following chapters.The third chapter is the serial correlation test of the predictive regression model.Based on the empirical likelihood method,a predictive regression model is considered,and the test statistic is constructed by the Jackknife empirical likelihood method.The asymptotic distribution of the test statistic under the null hypothesis and the local alternative hypothesis is derived.Finally,random numerical simulation is used to verify the finite sample properties and test power of the test statistics.In the fourth chapter,based on the Jackknife empirical likelihood ratio test statistic proposed in the third chapter,the actual data is used to analyze,in order to verify the validity of the test statistic.The fifth chapter is the conclusion and prospect,which is mainly to make a summary of the previous serial correlation test,and to look forward to the problems and unsolved problems.