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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?

Hans
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    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] – Pleb Jun 07 '22 at 09:15
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    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] – Pleb Jun 07 '22 at 09:15
  • @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. – Hans Jun 07 '22 at 19:49
  • Judging from our discussion in the comments under my answer, your question is unclear. Would you mind elaborating? – Richard Hardy Jul 02 '23 at 09:38

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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.

Richard Hardy
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  • I mean to estimate the realized volatility from the high frequency price/tick data. – Hans Jun 06 '22 at 14:01
  • @Hans, if realized volatility is itself an estimate of volatility, why do you want to estimate the former rather than the latter? – Richard Hardy Jun 06 '22 at 14:09
  • 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"? – Hans Jun 06 '22 at 17:23
  • @Hans, the former ~ realized volatility (an estimate), the latter ~ volatility (the underlying parameter). – Richard Hardy Jun 06 '22 at 17:31
  • The underlying parameter of what, some model? – Hans Jun 06 '22 at 17:48
  • @Hans, parameter of the data generating process. There is some distribution there, we do not know what it is, but it has a standard deviation and we are after it. (Strictly speaking, this might not be that simple, but I am inclined to simplify for now.) – Richard Hardy Jun 06 '22 at 17:50
  • Let us continue this discussion in chat. – Hans Jun 06 '22 at 17:54
  • I replied to you in the chat. – Hans Jun 08 '22 at 03:48
  • @Hans, I was going through my old answers and noticed this one was neither accepted nor upvoted. Did we solve the problem, or does the answer remain inadequate for your needs? – Richard Hardy Apr 17 '23 at 10:50
  • You did not seem to understand the question. Judging from the chat, you at first did not realize that the volatility was not given and needed to be estimated from the tick data. But finally you acknowledged the need to estimate the volatility. But that was just understanding what the question was but was yet to start solving the problem. – Hans Jul 02 '23 at 07:12
  • @Hans, that characterization is about the opposite of how I view our discussion. I never said the volatility was given (observable from the data) and I maintained throughout that it needs to be estimated. Meanwhile, you did not seem to show much appreciation for the idea that we are estimating parameters of a statistical model of the data generating process from which the observed data has been generated. Without this fundament, concepts such as realized volatility and the GARCH model lose ground. – Richard Hardy Jul 02 '23 at 09:34