Extended Modeling, Properties And Application About Semi-parametric Models With Martingale Difference Errors

In this thesis, we consider the properties of semi-parametric model with martin-gale difference errors. Because martingale difference sequences are not so strict as i.i.d. sequences, time series with martingale difference errors are possible to apply in broad-er fields. First we briefly introduce some usual time series, including usual parametric models and nonparametric models. Then, we raise the concept of semi-parametric mod-els to extend the application of both parametric models and non-parametric models. The semi-parametric models combine the two models together, and it can be expressed as yi=xiβ+g(ti)+εi. In this thesis, we study the kind of semi-parametric models with martingale difference errors.Firstly, we get both the least squared kernal estimations of parameter β and non-parameter g(-) in our model. Then we consider the r-th mean consistency and empirical likelihood of β and g(·). While proving the validity of semi-parametric mod-els, we consider Ljung-Box Q test, thus we can get the rejection region easily and then strengthen the practicability. Secondly, we use Matlab to generate data and compare dual non-parametric models and semi-parametric models. Then in this Mente Carlo experiment, we can see that semi-parametric models have a much smaller Mean Ab-solute Error(MAE) and fit the data well. At last, we use our model in practice. We choose the GDP data of China from1978to2011to compute, of course, the model fits well.