Portmanteau Test Of Empirical Likelihood Of Jackknife Based On Predictive Regression Model And Its Application

General regression models often assume the following conditions in practice: linear relationship between independent variables and dependent variables,mutual independence of error terms,mutual independence of independent variables,variance of error terms is constant,and normal distribution of error terms.The traditional predictive tests generally assume that the sequence of random disturbance terms follows independent and distributed structure,that is,there is no sequence correlation.However,if the random disturbance terms are sequentially correlated,it may lead to the failure of the parameter estimators of the model,thus making the statistical test of the model based on the parameter estimators invalid,which will also have a negative impact on the statistical inference.In addition,it is generally assumed that the correlation coefficient of error vector sum is zero in the predictive regression model,but the correlation coefficient is often not zero in the practical application.This results in nested endogeneity of the predicted regression model,resulting in biased coefficient estimation of the model,which leads to the failure of the traditional T-test.The appearance of strong sequence correlation may also mean that the model has errors.With the deepening of research,predictive regression models have been widely used in various fields,including finance,economy,biology,etc.Considering that the actual sample data structure is often unsatisfactory,it is of certain research significance to consider the correlation between the error terms of predictive regression models and conduct serial correlation test.In the widely used predictive regression models,the random error term is usually assumed to be independent and uniformly distributed,however,this presents two potential problems.First,assuming the independent isodistributive error term ignores the existence of nested endogeneity,which is evident in many practical applications.At the same time,in this case,any possible serial correlation in the random error term is not taken into account,resulting in estimation bias and statistical inference distortion in the forecast regression.Therefore,it is important to check the existence of such sequence correlation in advance.However,traditional Portmanteau tests,such as Box-Pierce(BP)and Ljung-Box(LB)tests,do not perform well under possible nested endogeneity.On this basis,a new combination test based on split sample and Jackknife empirical likelihood was developed to determine the possible sequence correlation of predictive regression under nested endogeny.The asymptotic distribution of the proposed test statistics is derived.Monte Carlo simulation shows that it has good finite sample performance.Finally,the proposed test statistic is used for pre-test in the empirical study,in which 11 financial variables are selected to predict the excess return of the S&P 500 index,and the empirical study shows the validity of the test statistic.In general,this thesis proposes a new method to pre-test the serial correlation of predictive regression models.The test is based on sample splitting,with half of the samples used to estimate unknown parameters of the predictive regression model to obtain residuals and the other half used to construct pseudo-observations that form the basis for the empirical likelihood of applying the Jackknife.The results show that this test has asymptotic Chi-square property and performs well compared with the traditional Portmanteau test.The proposal of this test statistic not only deepens the research of Portmanteau test but also further expands the application range of prediction regression model,which is of great significance to the research of some empirical data.This thesis is divided into five parts.The first chapter mainly introduces the current research background and significance of predictive regression model,and summarizes the research status of the model,hypothesis testing and methods studied in this thesis,from which the research ideas and framework as well as the research innovation points and difficulties are inspired.The second chapter mainly focuses on the preparatory knowledge required by readers to read and understand this article.The third chapter focuses on the construction process of the test statistics,the theorem proving process obeying asymptotic distribution and the numerical simulation process.In Chapter 4,the test method is applied to the actual data to verify the reliability of the numerical simulation and the robustness of the test statistics.The last chapter is the summary of the research content and the prospect of the future research direction.