# Order flow intensity

I am interested in how to calculate order flow intensity. I got access to high frequency data and can simulate a limit order book. What is the best approach if I want to calculate order flow intensity?

• You need to specify what you mean by the intensity. – LazyCat Feb 28 '16 at 3:31

Have a look to this paper, the methodology is well defined: Simulating and analyzing order book data: The queue-reactive model, by Huang, L and Rosenbaum.

You need first to define properly the events of which you want to estimate the intensity. I would suggest

• insert
• cancel
Then for each available tick of price $p$ (not each limit):
• normalize its size $Q_p$, for instance dividing it by the average limit order size, and rounding: $N_p:=[Q_p/L]$
• take $dt$ as the time to the next event affecting this queue $p$
• record the type of the event ${\cal T}\in\{$ insert, cancel, market$\}$
• just compute as estimate of $\lambda(p,{\cal T})=\mathbb{E}(dM(p,{\cal T})/dt)$: $$\hat\lambda(p,{\cal T}):=\frac{\#\{e(\omega)={\cal T}, N_p(\omega)=N \}}{\#\{N_p(\omega)=N \}}\cdot\frac{1}{{\rm mean}(dt(\omega)|N_p(\omega)=N )}$$
See the paper for exact definitions, but they are quite obvious: $\omega$ is "any event", and $\#\{ \cdot\}$ is the cardinal of a set. Since the paper has been published in the Journal of the American Statistical Association (110.509 (2015): 107-122), the statistical aspects are quite well defined.