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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 : $$y_t=\mu + \phi y_{t-1}+e_t $$ $$e_t \sim N(0, \sigma^2_t)$$ ...

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