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I have high frequency data for financial stocks (5-minute periodicity) and I want to forecast volatility.

I'm familiarized with the usual ARCH/GARCH models and their variants for daily data but after doing some research I've learnt that these models don't work well with high frequency data.

Which model is best for volatility forecasting when I have one data point every 5 minutes? Are there any known Python implementations of that model?

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  • $\begingroup$ There is a good selection of different high frequency (HF) volatility models documented in academic literature. One of them is the Realized GARCH model that extends the original GARCH model by incorporating additional information procured from HF data. I talk about it, in my answer here which also contains links to the original paper and papers of alternative HF models (HAR, HEAVY). Another model is the Heterogeneous Autoregressive (HAR) model of Corsi, that is also gaining popularity due to its increased parsimony. [1/2] $\endgroup$
    – Pleb
    Commented Jul 27, 2022 at 10:25
  • $\begingroup$ As with the GARCH models, the HAR model has an extensive family of alternative parameterizations attempting to explain different stylized facts inherent in intraday data. One of such alternative models, is the Semi-variance HAR (aka. SHAR) model of Sheppard that disentangles the realized variance into realized semi-variances. I have an answer here detailing the SHAR model. You might find some ad-hoc Python implementations of the models on Github. It also seems that the arch package has a HAR implementation you might be able to use. [2/2] $\endgroup$
    – Pleb
    Commented Jul 27, 2022 at 10:27
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    $\begingroup$ Thanks Pleb, amazing references! $\endgroup$
    – wlog
    Commented Jul 27, 2022 at 13:50

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I did my MSc thesis on this topic and found nonparametric methods such as SVR and RF outperform classic econometric specifications (ARCH, GARCH, EGARCH ect.). Similar results are found in the literature and nonlinear relations as well as fat tails are often cited as possible culprits.

Might be worth it to take a look at what happens when you plug your desired lags in a model like that!

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  • $\begingroup$ "classic econometric specifications", just to get some clarity: did you compare classic (G)ARCH models estimated on daily data, on intraday data or their well-developed realized counterparts (that uses both intraday and daily data) as provided in Hansen et al. (2012) paper? Also, your answer could benefit with some additional links to the literature you're referring to :-) $\endgroup$
    – Pleb
    Commented Jul 27, 2022 at 17:54
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We study exactly this in Endogenous Dynamics of Intraday Liquidity, by Bińkowski and L (the preprint is there).

My recommendation is to start with a AR (auto-regressive) model, and then to expend it. You should see that is you introduce other variables in a VAR (vectorial auto-regressive) version of this model, the needed lags will decrease, like if the recent traded volumes (and other liquidity variables) contain information on the less recent volatility.

In the past I used LSTM (a neural net version of ARMA) too, that was more useful for volumes than for volatility (especially if one want to learn the correct lags to be used).

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