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I have a project in which I'm given the state of the order book for a stock every 1ms, and I need to predict the return on the stock 2 minutes in the future using this information. I haven't been able to find good resources on this type of problem: time series forecasting in an online setting.
Does anyone have any book recommendations on this? Preferably, the book would be focused on financial time series.
What does "state of the order book" mean? Besides the best bid and ask, what other information does your data contain? E.g. depth of the book? If so, how many levels?
How it "return" defined? Buy at the best ask and sell at the best bid two minutes later? At this granularity, price impact may matter. Depending on order size and size of the queue, you may not be able to fill your sell order at the best bid.
Besides these context-specific questions, for forecasting price movement at this frequency you should start with simple models (e.g. ARDL models with appropriate LOB variables as regressors). At this frequency, price movement is mostly due to trading algorithms reacting mechanically to the state of the LOB in some prescribed manner.
You may want to consider the two sides of the LOB separately. In that case a simpe VAR (multivariate version of ARDL) would be a good starting point.
(Consideration of filtering models would suggest you have reason to believe there are unobserved systemic driver among the trading algorithms.)
Relevant info on forecasting using AR/ARDL/VAR can be found in probably any introductory text on time series, as well as online.
If you are interested in forecasting time series data you should follow Rob Hyndman and his blog https://robjhyndman.com/hyndsight/. Start by reading his book Forecasting: Principles and Practice. You can find an online free version here https://otexts.com/fpp3/.
Then if you are interested in Financial data, I suggest you Rue Tsay Financial Time Series book, and finally (but you have to master the math before otherwise it will be very painful) you can approach the bible of time series analysis: J.D. Hamilton Time Series Analysis.
These are off course just some hints, there is also the M Forecasting Competition of the Internation Institute of Forecasting that produces a lot of very useful resources. It focuses on the practical part of forecasting with the most up to date algos.