A time varying GARCH(p,q) model and related statistical inference

We propose a two-step local polynomial and a weighted bootstrapped estimator for the parameter functions of a time varying GARCH( p , q ) model. We also suggest a test statistic for testing the constancy of parameter functions of the model. Asymptotic distributions of the estimators and a test statistic are derived. The validity of the bootstrapped estimator and the test is established with the help of a simulation study.