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You have to use a multivariate Garch indeed. Search for mGARCH versions like GARCH-BEKK or VECH GARCH or DCC.


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If you just want a confidence interval for the sigma squared produced by the garch notice that the most popular approach is to assume that the distribution of the estimator is unknown and, as such, use non-parametric methods like bootstrapping. For more info read this answer which is also consistent with other sources like this . On bootstrapping meaning I ...


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Yes. We should indeed say that the Garch part of the model does not help to predict the Direction of the movement (this is given by the expected drift of the Arma, which gives the conditional mean of the return process) but helps to predict the size of the deviation of the next period return from the expected Arma drift. It is a measure of the squared size ...


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