Combining Overlapping Directional Forecasts for Optimal Trading
Summary
The document frames a trading problem in which an oracle repeatedly predicts whether an asset’s price will be higher or lower at a fixed future horizon. Each forecast has a stated accuracy rate, and the question assumes that absolute price-change magnitudes are the same across correct and incorrect predictions in either direction. A simple baseline opens a separate position for each forecast and closes it when that forecast’s horizon ends.
The central issue is that forecasts arrive more frequently than the horizon and are therefore dependent: earlier forecasts still contain information relevant to the current decision. The question seeks a method for combining this overlapping information rather than treating every signal independently, and mentions temporal-difference learning as a possible but uncertain direction. It offers no proposed solution, tested strategy, or performance evidence. Any practical approach would need to account for forecast dependence, position overlap, and trading costs, which the document does not specify.
Key ideas
- The oracle supplies directional predictions more frequently than the forecast horizon.
- Treating each signal as an independent trade creates overlapping positions and ignores information from earlier forecasts.
- The document assumes equal absolute price-change distributions across correct and incorrect predictions.
- It asks how to combine dependent forecasts but does not provide or evaluate a solution.
Tags
Full text
# Optimal trading given frequently delivered directional forecast # Optimal trading given frequently delivered directional forecast I am interest in trading by optimally exploiting a directional forecast given by an oracle. The oracle predicts directionally the price of an asset (higher or lower than at the moment of forecast delivery) in a forecast horizon H, say 180 minutes. The forecast is delivered several times within a single forecast horizon: it is delivered every D minutes, say, 20. It is known that: - The oracle is correct a certain fraction of the time, say 60%. Furthermore, let's make the simplifying hypothesis that: - The distribution of the absolute value of the realized price change is the same for all 4 pairs: [predicted up - right, predicted up - wrong, predicted down - right, predicted down - wrong] A trivial strategy to exploit this oracle would be to treat every single forecast independently, and execute a trade in the direction of the forecast at every delivery, closing each order after its forecast horizon has expired. Nevertheless, the forecasts predict quantities that are all but independent of one another (consecutive price points of the same asset at a frequency of 1/D). The forecast formulated at time T-D, for example, is relevant information when deciding what to do at time T, because it informs about the price at T+H-D, which in turn is very much predictive of the price at T+H. How can I exploit completely all the relevant information available? I tried looking into reinforcement learning techniques such as Temporal Difference Learning, but I can't find the perfect fit. Where should I look?
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