I have just run a DCC GARCH model in R and am trying to interpret the output. I have run the model with 3 time series. I know that alpha and beta tell about the short- and long-term spillover effect. However, I only get one dcca1 and dccb1 even though the values of dcca1 and dccb1 should be different for the different time series. So what do dcca1 and dccb1 tell me?

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Unfortunately, most of your interpretations are mistaken.

- DCC model does not allow for volatility spillovers. If you want a model that does, consider e.g. the BEKK model.

- dcca1and- dccb1are the two parameters of the DCC equation that show the relative weights of standardized errors at time $t-1$ (- dcca1) and the conditional correlation matrix at time $t-1$ (- dccb1). There are no other parameters specific to the DCC. The other parameters you see in the R output are from the individual conditional mean equations (the ones ending with- mu) and the conditional variance equations due to GARCH (the ones ending with- omega,- alpha1and- beta1). For more details, see p. 3-5 of the- rmgarchvignette.