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currently I am working with GARCH Modells. And it came to my attention that for the parameter estimation Maximum Likelihood approaches are commonly used. However I was wondering why Least Squared approaches are not in use. And I came up with the following explanation from Rachev in Financial Econonmetrics: enter image description here

Seems like due to this "strong condition" a Maximum Likelihood approach is more promising. Unfortunately I don't understand the condition. What does it mean and what are the implications? And why is the 8th-Moment important to an GARCH Modell?

Thanks a lot in advance, Clemens

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  • $\begingroup$ I think this fits better at Cross Validated. I suggest it to be moved there. (If the moderators agree to migrate the question, that could be better than just cross posting there.) $\endgroup$ – Richard Hardy Aug 8 '16 at 19:50
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    $\begingroup$ Least squares (LS) requires the data to be observable. Volatility (the dependent variable of GARCH models) is latent; therefore, LS cannot be applied directly. (Probably there are workarounds for estimating GARCH models that employ LS somehow, but that happens indirectly.) $\endgroup$ – Richard Hardy Aug 8 '16 at 19:54

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