Unified Test For The Intercept Of A Predictive Regression Model

Time series analysis is based on probability statistics as a theoretical basis to analyze random data sequences,and to establish a mathematical model,that is,to classify the model and estimate the parameters.We often use a variety of models when analyzing time series,including Autoregressive model,Moving Average Model,and Autoregressive Moving Average Model,Predictive Regression Model,Autoregressive Conditional Heteroscedasticity Model and other models,among which predictive regression model is the most widely used model in many time series models.The predictive regression model is often used to deal with predictability issues in the economic and financial field,such as the assessment of mutual fund performance,asset allocation optimization,conditional capital asset pricing,etc.,which are used to test the predictability of return on assets.In terms of the predictability of the return on assets of the predictive regression model,Zhu,Cai and Peng(2014)conducted a consistency test on the predictability of return on assets,that is,without considering whether the autoregressive sequence is stationary or unit root or It is a near-unit root process,constructing a consistent statistic to test and analyze the predictive regression coefficients.However,we find that Zhu,Cai and Peng(2014)respectively propose regression coefficient test methods for the case where the intercept term is known and unknown,which means that Zhu,Cai and Peng(2014)can predict the predictive regression model.The sex test needs to know the information of the intercept item in advance.We know that the existence of the intercept term will greatly affect our choice of the model,so the study of the intercept term will help us improve the accuracy of our selection.At the same time,we consulted the literature and found that domestic and foreign scholars have little research on the intercept items of time series models,and the sequences have different limit distributions under different conditions.This will hinder us from studying the intercept items,so it is necessary to the intercept term is tested for consistency.Therefore,this paper develops a consistent test for the intercept term of the predictive regression model by using the empirical likelihood method.As a kind of nonparametric method,the empirical likelihood method has been favored by scholars because of its universality and validity.Therefore,the empirical likelihood method is applied to various time series analysis models.This paper applies the empirical likelihood method to the predictive regression model and test its intercept term.The corresponding test statistic is constructed for the predictive regression model,and the asymptotic chi-square distribution of the corresponding empirical likelihood ratio statistic is obtained.Then,the corresponding simulation experiment and real data application analysis are carried out to verify the feasibility and practical application effect of the proposed test method.The stochastic simulation results show that the confidence probability of unified statistics is close to the set confidence level,and empirical analysis shows the feasibility of applying unified statistics.In addition,the proposed unified test method is extended and applied,and the model selection for predicting the regression coefficient of the regression model is provided to improve the test accuracy.By using the empirical likelihood method to conduct a unified test on the intercept term of the predictive regression model,the proposed unified test statistic can eliminate the need to distinguish the sequence {(3},which expands the new path for the related research of the intercept term.At the same time,the unified test of the intercept term can provide model selection for the test of the regression coefficient of the predictive regression model,and improve the test accuracy of the regression coefficient.The specific chapters of this paper are arranged as follows:The first chapter is the introduction of the article.This chapter mainly discusses the research background and significance of the article,the research status and research ideas at home and abroad,as well as the innovations and challenges.The second chapter is the theoretical basis of the article.This chapter is a detailed introduction to the theoretical knowledge of time series analysis,hypothesis testing and empirical likelihood method,laying the foundation for the following chapters.The third chapter discusses the empirical likelihood test of the intercept term of the predictive regression model.We construct an estimation function suitable for the predictive regression model,and obtain the test estimator is the asymptotic chi-square distribution,and carry out simulation experiments on the test statistic of the predictive regression model model to verify the feasibility of the test statistic.The fourth chapter is empirical research and analysis.This chapter uses the data of the CRSP database for empirical analysis and verification.This chapter first describes the data,and then uses the data to conduct a consistency test.The test results show that the consistency test method we proposed is of practical significance.Finally,we summarized this chapter.The fifth chapter is the conclusion and prospect of the article.This chapter is mainly to summarize the whole article,pointing out the shortcomings in the text and looking forward to it.