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You can use RATS software in which VAR GARCH is inbuilt function with CCC, DCC VECH and BEKK for co-variance estimation.

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Welcome to quant.SE! I do not have specific experience with the CARR Model, however, I had a short look in the paper you mentioned: As far as I understand the model specification you just implement a GARCH(p,q) estimation for the range $R_t:=\max{P_\tau}-\min{P_\tau}$ where $\tau=t-1,t-1+\frac{1}{n},\dots,t$ where $n$ is the number of intervals used in ...

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$D_{n}$ are the dummy variables taking a value of one from each point of sudden change of variance onwards, and $d_{n}$ are the estimated coefficients in relation to these breaks. So to apply your model: 1- Find the breaks using the ICSS algorithm. 2- Apply a garch model to your data by including dummy variables obtained in (1) in the conditional variance ...

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