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GARCH model is used to model persistence in volatility. If you square demean exchange rate and calculate autocorrelation you will find significant autocorrelation upto many lags that indicates the clustering of volatility in data. A simple ARMA(1,0)-GARCH(1,1) model can be written as : $$y_t=\mu + \phi y_{t-1}+e_t $$ $$e_t \sim N(0, \sigma^2_t)$$ ...


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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