# Growth of Order Book size during day

I am trying to find market-structure research on how the size / depth of the order book changes during the day for equities.

I would expect it to get deeper and deeper and bigger and bigger continously as the day progresses, but I don't have access to order book data to validate this.

Can someone here provide any insight on this topic? Hope this is question is applicable to this site.

For my purposes, I am mainly interested in two things:

1. What type of function gives a view of how it grows? Is it logarithmic? Linear? I'm guessing it's linear. Does the growth rate change during the day (for example, much higher in the beginning and towards the end)?

2. The distribution of the growth among different price levels. For example, will the ratio $$\frac{\mbox{number of quotes far-from-midpoint}}{\mbox{number of quotes close-to-midpoint}}$$ grow as the day progresses, or does it virtually stay the same?

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Yes, the order book grows. Is there something more specific you are looking for? –  chrisaycock Aug 8 '13 at 13:04
Thanks. I've updated the question. –  UmaN Aug 8 '13 at 14:46
Why would you guess it's linear? I can't think of any a priori reason to think it's linear. –  user2763361 Dec 8 '13 at 14:31

We just issued a paper studying and modelling orderbook dynamics, especially the way they replenish or empty Simulating and analyzing order book data: The queue-reactive model. We disclose the way the first queue evolve with respect to the size of others (best opposite and second or third queues).

Other recent papers complement ours:

For intraday seasonalities analysis, have a look at Chapter 3 (From Intraday Market Share to Volume Curves: Some Stationarity Issues) of Market Microstructure in Practice.

Look at Figure 8 of the paper:

On the x-axis you have the current size of the first queue (in Average Event size) and on the y-axis you read an intensity. Three colours figure the state of the best opposite queue (i.e. the best ask if you consider the best bid): in bleue for small sizes, green medium sizes and red large sizes:

• Upper right chart gives you the limit order insertion flow
• Upper left one the cancellations
• Lower left the market orders
• and lower right the ratio you have in mind (one means "nothing changes", lower than 1 the queue decreases, larger than one it increases).
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