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Can one use the GARCH model to estimate the realized variance/volatility, such as done in this paper, rather than forecast the volatility, from (high frequency) price/tick data?

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    $\begingroup$ While your mentioned paper is from 2002, there has been a recent rise in realized GARCH models, which utilize realized estimates procured from high-frequency data to further predict and estimate the ex-post volatility. Be aware that realized measures only estimates the ex-post variation within each day and not across days. Therefore, you need a model-based construction that utilizes realized measures and thus “links” the estimates across days, in order to capture some of the stylized facts of financial time-series. [1/2] $\endgroup$ Commented Jun 7, 2022 at 9:15
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    $\begingroup$ Eg. One of such model-based constructions is the HAR model, that linearly links different averages of realized estimates. The Realized GARCH model is another one of these constructions. I have done a detailed answer of the Realized GARCH model that gives you an introduction to the construction of the model and further contain links to different papers that might be of use, if you want to estimate ex-post volatility using realized GARCH models. I am not completely sure if this is what you’re looking for, hence the extended comment. [2/2] $\endgroup$ Commented Jun 7, 2022 at 9:15
  • $\begingroup$ @Pleb: Thank you very much for the extended comment. Yes, I do want to estimate ex-post volatility using GARCH model. If it is the realized GARCH model that accomplish this task, then that is it. I am checking out your linked answer. $\endgroup$ Commented Jun 7, 2022 at 19:49
  • $\begingroup$ Judging from our discussion in the comments under my answer, your question is unclear. Would you mind elaborating? $\endgroup$ Commented Jul 2, 2023 at 9:38

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You can use GARCH to estimate volatility. If you have high-frequency data, you can use realized volatility to estimate volatility. You would normally not use GARCH to estimate realized volatility (why estimate an estimate?), though I suppose it is technically possible to view your fitted volatilities from a GARCH model as estimates of realized volatilities.

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  • $\begingroup$ I mean to estimate the realized volatility from the high frequency price/tick data. $\endgroup$ Commented Jun 6, 2022 at 14:01
  • $\begingroup$ @Hans, if realized volatility is itself an estimate of volatility, why do you want to estimate the former rather than the latter? $\endgroup$ Commented Jun 6, 2022 at 14:09
  • $\begingroup$ I do not know what you mean. Volatility is not directly observable but estimated either by realized volatility from the price data or from the implied volatility of the associated options. What do you mean by "the latter"? $\endgroup$ Commented Jun 6, 2022 at 17:23
  • $\begingroup$ @Hans, the former ~ realized volatility (an estimate), the latter ~ volatility (the underlying parameter). $\endgroup$ Commented Jun 6, 2022 at 17:31
  • $\begingroup$ The underlying parameter of what, some model? $\endgroup$ Commented Jun 6, 2022 at 17:48

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