Estimation Of Parameters Of TARCH(q) Model

In our paper, we study the statistical inference of Threshold ARCH (TARCH) model under no-restriction and restriction conditions. First, we give the Least Squares Rule and Maximum Likelihood Rule, and we use the Empirical Process Theory method to testify the strong consistency of parameter estimations under these rules. Second, we get the asymptotically normal by virtual of martingale central limit theorem. We should illuminate that in literature, the auther have given the asymptotically normal of parameter etimations under the Least Squares Rule, which is similar to us, however, we get the further result about strong consistency, and we study the asymptotically normal and strong consistency about MLE. At last, wo give an arithmetic about it.Next is the main frame of this paper.Chapter 1. Give some information about financial time series and ARCH model.Chapter2. Introduce TARCH(q)model and its financial background.Chapter3. Give the the Least Squares Rule and Maximum Likelihood Rule about TARCH model, and study the strong consistency.Chapter4. Give the asymptotically normal about these estimations.Chapter5. It is also the last chapter. We give the MLE under restriction of TARCH(l), and give an arithmetic.