Computing Features Across Multiple Frequencies
Multi-frequency feature construction combines signals computed at different sampling rates — daily, weekly, monthly — into a single model input, since fast and slow versions of the same idea often capture genuinely different information.
Prerequisites: Lag and Rolling-Window Features
A stock's 5-day momentum and its 12-month momentum are computed from the same underlying prices but tend to predict different things — the short version reacts to news and flow, the long version captures a slower trend. Multi-frequency feature construction is the practice of deliberately computing the same type of feature at several different time horizons and feeding all of them into a model, rather than picking just one.
The same underlying idea — momentum, volatility, mean reversion — carries different information at different horizons, so combining a fast and a slow version of a feature often adds more predictive value than optimizing either window in isolation.
The practical challenge is that faster features (daily) update every day while slower features (monthly) barely change between updates, so a model has to be built to handle inputs that refresh at genuinely different rates without accidentally weighting the more frequently updated ones more heavily just because they change more often.
Worked example. A model uses 5-day, 20-day, and 120-day price momentum for the same stock. On a given day these read +2%, +8%, and -3% respectively — short-term strength, medium-term strength, but a longer-term downtrend. Feeding all three into the model lets it learn combinations (like "short-term bounce inside a longer downtrend") that no single-frequency version of momentum could express on its own.
This approach is common in both traditional factor construction and modern tree-based or neural models, where the model itself is left to discover which frequency combination matters in which regime.
Further reading
- de Prado, Advances in Financial Machine Learning (ch. 2)