FAQ · Ensemble forecasting

What is ensemble forecasting?

Reviewed against the platform's code on Sep 26, 2026

Ensemble forecasting combines the forecasts of several models, or several runs of one model, into a single forecast, usually a weighted average. Because different models make partly different errors, the combination tends to be more accurate and more stable than a typical member, and the spread between members shows how much they disagree.

Why it matters

No single model is best in every period. Each one misses in its own way, and which one leads tends to change as markets change, so relying on one model means picking the winner in advance. Averaging cancels part of the errors the models do not share. Under squared error, a weighted average's loss equals the members' weighted average loss minus the weighted average of their squared distances from it (Krogh and Vedelsby, 1995). The combination is therefore never worse than the average member, and it gains most when members disagree. It is not guaranteed to beat the best member, and near-copies of one model add little.

How it works

Combining forecasts goes back to Bates and Granger (1969), who showed that a well-weighted mix of two forecasts can have a smaller error variance than either one. Weights can be equal, estimated from past errors, or learned by a second model (stacking). A simple average is hard to beat in practice, because estimated weights carry errors of their own: the forecast combination puzzle (Stock and Watson, 2004). Online aggregation instead updates the weights after every outcome. Bernstein Online Aggregation (Wintenberger, 2017) weights each model by its accumulated advantage over the combined forecast, minus a penalty on the squared advantages, so erratic skill earns less than steady skill. Its average loss approaches that of its best member in hindsight.

How Opulence Alpha applies it

Opulence Alpha combines up to nine model voices into each stock forecast: CatBoost, LSTM and quantile forecasting models, a sector model, and five voices derived from its fair-value engine. Not every voice speaks at every horizon. Bernstein Online Aggregation sets their weights separately for each horizon and for each combination of market regime, volatility regime and sector; a thin combination leans on a broader estimate. Each voice is scored daily on its rank correlation with the returns that followed. Older evidence fades, and a small fixed share keeps every learned weight above zero. Voices whose forecasts move together are discounted by their correlation. The blend is a weighted mean, and disagreement between voices widens its uncertainty instead of cancelling out.

Which models are combined, and how →

Related concepts

Probabilistic forecastingProbabilistic forecasting publishes a distribution of possible returns, with calibrated intervals, instead of one expected number — so a position can be sized from its uncertainty.Information coefficientThe information coefficient (IC) measures how well a signal ranks stocks: its correlation with the returns that followed, across stocks each date, averaged.Conformal predictionConformal prediction turns any forecast into intervals with a stated coverage, sized by the model's measured errors on held-out data, not by an assumption.Market regime detectionMarket regime detection classifies the current market state — volatility, credit, liquidity, policy, the business cycle — so strategies and risk can adapt. How nine axes and a hidden semi-Markov model do it.
All concepts →Sector behaviour in every market regime →

Questions

Why do ensembles beat single models?

Because models make partly different mistakes, and averaging cancels the part they do not share. Under squared error a weighted average is never worse than its average member, and it gains more the more the members disagree. It is not certain to beat the best member in every period, but it removes the need to know in advance which model that will be. The gain shrinks when the members are near-copies of each other.

What is Bernstein Online Aggregation (BOA)?

An online method for combining forecasts, introduced by Wintenberger (2017). After each outcome it compares every model's loss with the loss of the combined forecast. A model's weight grows exponentially with its accumulated advantage over the combination, minus a second-order term on the squares of those advantages, so steady skill earns more trust than erratic skill. Its guarantee holds for any sequence of bounded, convex losses, with no model of how the data were generated.

Should ensemble weights be equal or learned?

Equal weights are a strong baseline, because weights estimated from a short history add noise of their own; that is the forecast combination puzzle. Learned weights pay off when some models are persistently better, or when skill shifts between models over time. Online methods address the second case: forgetting old evidence lets the weights follow a change, and a small floor lets a model that fell out of favour earn its way back.

How many models does Opulence Alpha combine?

Up to nine voices: CatBoost, LSTM and quantile forecasting models, a sector model, and five voices derived from the fair-value engine. Fewer speak at 1 and 5 days, because three of the valuation voices forecast only at 21 and 63 days. A voice whose latest model fails the separate statistical gate on held-out data is still scored every day, but it does not shape the published forecasts.

References

  • Bates, J. M. & Granger, C. W. J. (1969). The Combination of Forecasts. Operational Research Quarterly, 20(4), 451–468.
  • Krogh, A. & Vedelsby, J. (1995). Neural Network Ensembles, Cross Validation, and Active Learning. Advances in Neural Information Processing Systems 7, 231–238.
  • Stock, J. H. & Watson, M. W. (2004). Combination Forecasts of Output Growth in a Seven-Country Data Set. Journal of Forecasting, 23(6), 405–430.
  • Wintenberger, O. (2017). Optimal learning with Bernstein Online Aggregation. Machine Learning, 106(1), 119–141.

Educational content about research methods. Not investment advice.