Choosing a Forecast Horizon for Limit Order Book Price Labels

Summary

The document defines a supervised-learning target for limit order book data using the mid-price, calculated from the best ask and best bid. Each book update is treated as an observation, and the target records whether the mid-price rises, falls, or stays unchanged over a future horizon. That horizon can be specified as a fixed number of book events or as a fixed amount of elapsed time.

The question asks what value of the horizon is reasonable, but the included response stops before giving guidance. The excerpt therefore establishes the labeling concept without offering a selection method, empirical comparison, or recommended value. In practice, a horizon choice would need to match the intended prediction or execution task and the data’s event rate; the document itself does not resolve that choice. It also provides no results showing how different horizons affect label balance, forecast accuracy, or trading performance.

Key ideas

• The mid-price is defined as the average of the best bid and best ask.
• Each limit order book update can be labeled by the future direction of the mid-price.
• The forecast horizon may be measured by elapsed time or by a count of book events.
• The excerpt poses the horizon-selection question but does not include an answer or evidence comparing choices.

Tags

# Find a reasonable h


# Find a reasonable h












> 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 by LazyCat (score 1)

https://quant.stackexchange.com/a/39379

It depends on several things:

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.