The possibility of identifying nonlinear time series using nonparametric estimates of the conditional mean and conditional variance were studied in many papers. One of the main problems in these papers is development of time series methods of analysis through regression models even without knowing the regression function. The article deals with the estimation of copula-based semi parametric models for GARCH (1, 1) processes with usual kind of information about the distribution law. These models are characterized by conditional heteroscedasticity and have been often used in modeling the variability of statistical data. The basic idea is applied to a local linear regression with squared residuals for finding the unknown function.