Yes, GARCH is a parametric model(参数模型) of the volatility dynamics. More specifically, GARCH(1,1) is an AR process containing the previous squared error term and the variance of it. The most common methodology for estimating is the ML method. And semiparametric model(半参数模型) is another thing... It is commonly assumed to be a misspecified model of the real data, and has parameters to be estimated, like neural networks, random field, etc... I will not talk about the nonparametric model here...