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ARIMA and GARCH are old news for predicting volatility time series of asset returns. I am aware of papers that replace ARIMA and GARCH with machine learning algorithms to predict financial volatility more accurately, and so this question is a reference request for a survey of what's out there:

How do the performances of the following, and other, machine learning algorithms compare with one another, and GARCH, at forecasting volatility for horizons longer than just 1-day/step ahead?

  • random forest
  • support vector regression (SVR)
  • gradient boosting
  • K nearest neighbors, etc)

And are the machine learners also implemented in an autoregressive formula like GARCH (i.e. they use preceding historical volatility observations to estimate the current volatility)?

Also what do the research articles say regarding the theoretical reason for applying machine learning to volatility time series in particular?

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  • $\begingroup$ Are you more interested in predicting the realised volatility of the time series over a period (which is backwards looking, we don't know it until a period is over), or the implied volatility (which is implied by the market in the price)? If you're after implied volatility, is VIX prediction sufficient (as a single number encapsulating 'vol') or are you interested in the whole surface? $\endgroup$ – StackG 2 days ago
  • $\begingroup$ Just plain volatility of an asset's returns (the second statistical moment of a random variable), based on(the features being) historical estimates/realizations of itself, nothing about market proxies or derivative assets $\endgroup$ – develarist 2 days ago
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Just based on my understanding of the ML models themselves, I have a hard time believing KNN or RF are useful in anyway. They wouldn't be the first models I try and tend to just be ML models taught in class for who knows what reason honestly - maybe because they are easy to understand? From what I have read about ML in general (not in relation to time series), all of the ones you have listed have been outclassed by neural networks. Gradient boosting might be one that is still somewhat useful.

KNN looks to predict a value based on K observations that are most similar and then takes the average. Do you think tomorrow's volatility really is equal to the most similar days in your data set, even if the days are from 3 years ago? If so KNN, may be helpful.

RF is just a less good version of Gradient Boosting Trees. It predicts based on thresholds of features and as a result just partitions your data and then predicts based on the average of the average of many trees. So tomorrows volatility is equal to days when yesterday's vol is greater than x but less than y, snp moved by more than z but less than a, etc... Does that make sense? Maybe, but due to the partitioning nature of RF, it can never truly replicate any mathematical function. Meaning, if the true relationship between x and y is linear, a linear regression will always do better than a random forest.

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This largely depends on your setting and the available features.

You can include further information into classification or regression algorithms by providing the model with additional features such as the daily, weekly, monthly returns of previous periods and eventually also use these to create more features such as measures of volatility, mean-reversion or other aspects you would include in a "traditional" approach.

Benefits of machine learning algorithms (especially neural networks such as LSTMs or other RNNs) are, that they tend to be really fast and still offer a comparably good performance to many sophisticated option pricing models.

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  • $\begingroup$ ok i could incorporate features besides autoregressively using preceding volatility estimates, but how well has this worked in publications? Before even going to other features, how have distinct machine learners compared against one another when they only use preceding volatility estimates (autoregression) for features? Which ones perform better for forecast horizons longer than 1 day ahead? $\endgroup$ – develarist 2 days ago

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