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So I'm studying different ways for the Value at Risk calculation. Currently my attempt is in using the univariate Markov-Switching Multifractal framework. I've already estimated the $\hat{\sigma}_{t+1}$. But i'm not sure if the following formula for the estimated VaR one period ahead is correct.

$VaR_{t+1}(\alpha) = mean(-returns) + \hat{\sigma}_{t+1} .\Phi^{-1}(\alpha) $

Where $ \Phi^{-1}(\alpha)$ is the quantile function for the normal distribuition. Is this the correct formula?

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