EWMA

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If the initial sigma^2 value is not zero, the wobbly volatility line will very quickly attain its steady state.  Therefore, you can use much fewer data points and skip the heteroscedastic part.

But there is still the problem of clipping an unusual spike at the end of the series that can distort the one step ahead forecast.

It is important to get the one step ahead forecast right because you can use MC simulation to project further into the future.

 

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  • Another approach: set the initial sigma^2 equals to the squared of 1st observation, then compute the EWMA starting from observation two. This approach is presented in John Hull's Book on the Future & Options. 

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