On the Distribution Estimation of Power Threshold Garch Processes

The aim of this paper is to estimate the probability distribution of power TGARCH processes by establishing bounds for their nite dimensional laws. These bounds only depend on the parameters of the model and on the distribu- tion function of its independent generating process. The application of this study to some particular models allows us to conjecture that this procedure is an ade- quate alternative to the corresponding estimation using the empirical distribution functions, particularly useful in the development of control charts for this kind of models.