Parameters Estimation Of AR(p) And MA(q) Models From General Error Distribution

Time serial analysis theory, as a branch of mathematical statistics, has been appliedwidely in many fields. The main work is estimating the overall property through observinginformation. So it is of great importance to choose a proper model to express the time series.In the paper, we consider parameters' estimation in the situation thatε_t～GED(r) in AR(p)and MA(q) models.In the first chapter, we give a brief account of the time series background and introducespecially on stationary time series in the parameter estimation.In chapter 2, we discuss the parameters' estimation in AR(p) and MA(q) models underthe condition thatε_t～GED(r). In AR(p) model, the parameter from GED is known. If r＞1,log-concave adaptive rejection sampling method is used to estimate parameters; if r≤1,log-convex adaptive rejection sampling method is adapted. When the parameter from GED isunknown, we have to decide its range, also use the same method to give a reasonableestimation of the parameters. In MA(q) models, the likelihood function is more complicatedthat we just search a better estimate value in a certain range. Another method introduced isautoregression approximation method.Chapter 3, parameters are estimated in examples, using illustrations and tables to list theestimated results, more intuitively shows the estimated effect.Conclusion of this work is done to conclude the estimation method, moreover we discussthe feasibility and what we have to improve and explored in deep research.