Finite Estimation Of Moving Average Coefficient In MA (1) Model

Time series analysis is an important branch of statistics and widely used in other disciplines, especially in the economic field such as futures, stocks and securities,etc. It plays an important role for predicting the development trend and hedging risk in industry. This paper focuses on the statistical inference for the moving average coefficient of MA(1) model in finite sample and the results has an important significance to improve the research system of time series analysis.The main contents of this paper include the following parts:Firstly, this paper introduces the research background and the study significance and makes a comment of the domestic and foreign literatures from the perspective of the application and parameter estimator and coverage probability. In terms of this, the main content is proposed.The second part is the theoretical foundation which simply introduces the basic knowledge of the four common models in time series analysis and the moving average model.The third chapter is the part of statistical inference and is also the main part of this paper. It includes three sections. The first section is part of statistical inference in finite sample. The exact confidence region and the hypothesis test for moving average coefficient of MA(1) model are structured under the condition that the series mean of model is known or unknown. Simultaneously, the test for reversability of MA model is also discussed. The statistical inference for MA(1) model in large sample also is discussed under the same conditions. The asymptotic confidence region and hypothesis test for moving average coefficient are derived on the basis of likelihood ratio test. Finally, the exact and asymptotic confidence regions and hypothesis tests of the two parts are used to compare the excellent property in terms of coverage probability.The forth part is model generalization. In this chapter, the third chapter research results are extended to the generalized MA(1) model make the model can be morewidely used.Finally, the power function of hypothesis test in chapter three has been simulated by Monte Carlo method.The paper shows that the exact confidence region for moving average coefficient is better than the asymptotic confidence region based on the likelihood ratio test in terms of coverage probability.