What are the most common ways to model intraday trading volume, particularly for futures contracts? There are obviously a number of seasonal-type factors, like roll, economic news releases, time of day, etc. Are there any standard modeling techniques to deal with this type of problem, or any papers/books that are applicable?

• What do you mean by "modeling"? Econometric model to understand relevant features through testing? Machine learning model to forecast accurately? Theoretical model, SDE? Nov 16 '13 at 9:02
• Forecast trading volume at a particular time, e.g. for implementation of a simple VWAP algorithm Nov 17 '13 at 16:22
• what time horizon Nov 17 '13 at 16:36
• What works on a high frequency is compeltely different to low frequency Nov 18 '13 at 8:50
• Even at a high frequency, what works over 1 second is completely different to what works over 10 minutes. Nov 18 '13 at 12:41

The best paper is probably Relative Volume as a Doubly Stochastic Binomial Point Process - James Mcculloch. In this paper the volume is modelled via a Point Process, and theoretical laws are derived (with confident intervals, etc).

And we put elements about this in Market Microstructure in Practice, Chap 2.1. Volume curves are analyzed, not only during the intraday auctions (comparing the volume curves over the world in GMT), but the intensity of order sent during the prefixing auctions.

• Awesome. Can't wait for your new book! Nov 20 '13 at 1:46

From my point of view, dynamic models like the one developped in Relative Volume as a Doubly Stochastic Binomial Point Process - James Mcculloch to provide a dynamic forecast of the volume does not improve significantly the forecasting comparing to a static volume curve forecast using historical data (last month intraday data, and an EWMA algorithm).

I've done some analysis of this kind in the past, and i can tell that from a practical point of vue (algorithmic execution), static forecast provide good results, you will have to deal with macroeconomic days separately!

You can find a paper made by PragmaSecurities, Static VWAP: A Comparative Analysis, that deal with this subject for equities (but i think you can extrapolate it futures) : http://www.pragmatrading.com/sites/default/files/pdf/static_vwap_a_comparative_analysis_-_2009.pdf

• I agree with @user1646105 on the fact that the gain of implementing McCulloch approach can be discussed. Nevertheless in terms of modelling and important concept, almost all what is needed is in this paper. Nov 25 '13 at 12:53
• I agree totaly with @lehalle, on the fact that the mathematical approach on McCulloch paper is very interesting, and I also beleive that it's "a must to read" and know when you get deal an model intraday processes! Nov 26 '13 at 8:55