I have seen a plenty of articles/books regarding volatility forecasting applied to high frequency data, but none of them were dedicated to forecasting the actual prices (for example bid/ask of currency pairs, stock prices).
Forecasting Volatility using High Frequency Data (P. R. HANSEN, A. LUNDE)

I realize that forecasting hft data must be hard because of several problems:

  • How long model will be valid?
  • How to check such validity?
  • Will a new model be calculated on time? (NN and most of subtypes of NN need a lot of time to be recalculated)

Given the above mentioned problems/restrictions I would like to ask you:

  1. What's the best way of forecasting high-frequency data?
  2. What kind of scientific papers/books should I follow in order to be up-to-date in this topic?

Personal feedback:
From my own research based on hft data I can write that generally only few models are better than naive forecasting (but only in some sub time series - few minutes etc.)

  • Kalman Filtering (calibrated accordingly)
  • ARIMA, ARMA models

Generally worse than naive forecasting are:

  • Holts linear model (ARIMA (0,2,2)
  • Linear Regression
  • Exponential Smoothing
  • Moving averages (different types)
  • 3
    $\begingroup$ why would anyone in his right mind tell you how to predict, say, stock prices? $\endgroup$
    – LazyCat
    Commented Sep 9, 2015 at 15:58
  • $\begingroup$ I am not building a trading agent, basically I am doing a scientific research. I have shared my results and maybe someone will be willing to contribute to the topic and will share his thoughts and experience. $\endgroup$ Commented Sep 9, 2015 at 19:28
  • 3
    $\begingroup$ It doesn't really matter what you do, a question "how to predict stock prices" = "how to make money". Your feedback is meaningless, unless, you specify how do you apply your forecasting techniques. E.g. I would suspect that linear regression doesn't work for you not because it's a bad tool, but because you apply in it a wrong setting. Finally, to the best of my knowledge, most of academic research assumes some martingale condition for stock prices, which implies no forecasting. If you are not in this setting, it may be useful to specify your assumptions. $\endgroup$
    – LazyCat
    Commented Sep 9, 2015 at 20:42
  • 1
    $\begingroup$ I don't know about books but you can look at: market-microstructure.institutlouisbachelier.org/…. It's a a lots of conference on HFT mainly given by academics. You can look for the programme and google the name of the researcher, I think you can even download the powerpoints of the conference. the LPMA (french math laboratory) has a great team in HFT (Mathieu Rosebaum etc..) You look for them. $\endgroup$ Commented Sep 11, 2015 at 12:50
  • 1
    $\begingroup$ One recommendation: If you want to forecast high frequency data, you also need to take into account (and model) the strong periodicity behavior observed in intra-daily volatility (the "U Shape") , see Andersen, T. G., & Bollerslev, T. (1997). Intraday periodicity and volatility persistence in financial markets. Journal of Empirical Finance, 4(2-3), 115–158. doi.org/10.1016/S0927-5398(97)00004-2 $\endgroup$
    – Malick
    Commented Nov 26, 2015 at 0:09

2 Answers 2


A good place to start would be to understand the environment in which HFT takes place. What causes prices to form on the lowest possible level?

What mechanisms do exchanges use to process orders, how would they affect the price discovery process?

This in generally known as market-microstructure, and there is a lot of literature available on the subject, but you should also augment that with just physical observation of the orderbook, trades and the resulting price movements to get a better understanding of the whole process.

Once you have an understanding of what you are dealing with, you can start to build and test hypothesis.


at HF it is probably more important to guess the direction (up/down) than actual prices. For that you will have a lot of noise and financial time series have low signal to noise ratio. that is why classifiers (up/down) are the best practice in HF, not punctual predictors of prices. This has also to do with the computational complexity required to forecast a classifier vs a punctual value (simply put, in HF you need to cut down running time, thus computational complexity, in my experience many strategies fail due to implementation time and computational complexity). In any case, Kalman filters, ARMA, PCA, Fourier analysis are all good methods to extract signal. Once you have extracted the signal (i.e. removed most of the noise) then you should move on with other kind of models.


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