Combine Estimation Function Method Inference for Generalized Autoregressive Conditional Heteroskedasticity Models

This paper conducts a statistical study on the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model using the Combine Estimation Function Method (CEF). By applying the Estimation Function Method (EF) and the Combine Estimation Function Method (CEF), we obtain the parameter estimates for the generalized autoregressive model and prove that these Combine parameter estimates converge to a normal distribution. Numerical simulations are used to compare the statistical properties of the proposed parameter estimates. The simulation results indicate that the parameter estimates from the Combine Estimation Function Method are superior to those obtained by the pseudo-maximum likelihood method and the least squares method. Empirical studies also demonstrate the effectiveness of the Combine estimation method.