What is the difference between GARCH(1,1), AR(1)GARCH(1,1), and DCC-GARCH?
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An $AR(1)-GARCH(1,1)$ is a GARCH(1,1) model estimated from the residuals on an $AR(1)$
A $DCC-GARCH$ model is a particular type of multivariate $GARCH$ where some restrictions are made on the conditional covariance matrix, namely, it assumes it's form to be $H_t := D_t R_t D_t$ where $D_t$ is a diagonal matrix and $R_t$ is the simultaneous correlation matrix between the components
