# Unlabelled mid-price stock data

The mid-price at time $t$ is denoted by $$p_t = \frac{s_t^{a,1} + s_t^{b,1}}{2}.$$

This mid-price can evolve in minimum increments of half a tick but is almost always observed to move at increments of a tick over time intervals of a millisecond or less. In our feature set, each limit order book update is recorded as an observation. Each observation is labelled bases on whether the mid-price will increase, decrease or remain over a horizon $h$: $$Y_t = \Delta p^t_{t+h},$$ where $\Delta p^t_{t+h}$ is the forecast the discrete mid-price changes from time $t$ to $t+h$, given measurement of the predictors up to time $t$. The forecasting horizon $h$ can be chosen to represent a fixed number of events or can be a fixed time interval.

This definition is from A High Frequency Trade Execution Model for Supervised Learning (https://arxiv.org/pdf/1710.03870.pdf).

For trading on high price changes, how could I use this strategy to label my quote for Recurrent Neural Network training purposes? I don't even sure of the metric they use. It is High Frequency Trading, but I don't want to trade on low price changes. Here is an example of what I want eventually: First graph.

#=Quote,EventSymbol,EventTime,BidTime,BidExchangeCode,BidPrice,BidSize,AskTime,AskExchangeCode,AskPrice,AskSize
Quote,AKER,20180402-030000.001-0400,20180402-030000-0400,P,0.895,0,20180402-030000-0400,K,0.9,0
Quote,AKER,20180402-040000.089-0400,20180402-030000-0400,P,0.895,0,20180402-040000-0400,P,4,56
Quote,AKER,20180402-040000.089-0400,20180402-030000-0400,P,0.895,0,20180402-040000-0400,P,1.8,100
Quote,AKER,20180402-040000.089-0400,20180402-040000-0400,P,0.71,10,20180402-040000-0400,P,1.8,100
Quote,AKER,20180402-040000.089-0400,20180402-040000-0400,P,0.71,10,20180402-040000-0400,P,1.36,2
Quote,AKER,20180402-040000.090-0400,20180402-040000-0400,P,0.71,10,20180402-040000-0400,P,1.3,5
Quote,AKER,20180402-040003.727-0400,20180402-040000-0400,P,0.71,10,20180402-040003-0400,P,0.9,3
Quote,AKER,20180402-040053.231-0400,20180402-040053-0400,Q,0.8987,10,20180402-040003-0400,P,0.9,3
Quote,AKER,20180402-040737.956-0400,20180402-040737-0400,P,0.71,10,20180402-040003-0400,P,0.9,3
Quote,AKER,20180402-040737.956-0400,20180402-040737-0400,Q,0.8988,10,20180402-040003-0400,P,0.9,3
Quote,AKER,20180402-041017.146-0400,20180402-041017-0400,P,0.71,10,20180402-040003-0400,P,0.9,3
Quote,AKER,20180402-041059.737-0400,20180402-041059-0400,Q,0.8987,10,20180402-040003-0400,P,0.9,3
Quote,AKER,20180402-041339.757-0400,20180402-041339-0400,P,0.71,10,20180402-040003-0400,P,0.9,3
Quote,AKER,20180402-041339.758-0400,20180402-041339-0400,Q,0.8988,10,20180402-040003-0400,P,0.9,3
Quote,AKER,20180402-042349.831-0400,20180402-042349-0400,P,0.71,10,20180402-040003-0400,P,0.9,3
Quote,AKER,20180402-042349.831-0400,20180402-042349-0400,Q,0.8989,10,20180402-040003-0400,P,0.9,3
Quote,AKER,20180402-050327.037-0400,20180402-042349-0400,Q,0.8989,10,20180402-050327-0400,Q,0.987,60
Quote,AKER,20180402-050327.042-0400,20180402-042349-0400,Q,0.8989,10,20180402-050327-0400,Q,0.9,3
Quote,AKER,20180402-060137.419-0400,20180402-060137-0400,P,0.83,10,20180402-050327-0400,Q,0.9,3

• $a^2+b^2+2ab=(a+b)^2$ How can I use it to prove $x^n+y^n=z^n$ has no positive integer solutions for $n>2$? – LazyCat Apr 15 '18 at 2:14
• Fermat Last Theorem, but what is your point? – Jeremie Apr 15 '18 at 12:16
• Your question looks similar to my previous comment: put something obvious, like the definition of a midpoint price, and ask how to get something highly nontrivial from it - a predictive RNN. A bit more seriously, I've looked at that guy's papers before and heard some of his talks, and I have a very low opinion of his work. I think, it's mostly self-promotion using the buzz words everyone wants to hear: deep learning + HFT. There's very little substance in his papers – LazyCat Apr 15 '18 at 16:09