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To get it out the way: you cannot ask 'what model is better' without a reference to what its use is. Do you want to test for the mean or the AR parameter to trade it? Do you want to calculate VaR? Do you want to forecast volatility over one period? Or over 1000 periods? Or higher moments? Do you want to simulate volatility over one period? Or longer? For ...


I would keep the model with p=1 and q=1 even those the null hypothesis that ARCH-term's coefficient equals 0 was not rejected. The reason is that (generally) the less autocorrelations there are in the resulting serie, the more accurate your forecast will be. Indeed if you estimate a model and leaves some autocorrelation it means it is still possible to ...

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