Find a reasonable h

Question

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).

According to that definition, what would be a reasonable $h$ here?

Answer 1

It depends on several things:

1. Data: if your data has prices updated every hour, any h < 1 hour just doesn't make sense
2. Goal: in practice, if your looking to build a strategy, you'll be limited by your infrastructure. I.e. if you're using a retail broker, predicting for h = 10 milliseconds won't help you, since you can't update your quotes that frequently
3. Noise: generally, the shorted the horizon, the less noise you'll have in your observations, but something ~ 1min should be good enough.