Forecasting is estimating a future outcome using information available when the estimate is made. A quant may forecast a return to size a position, volatility to set a risk limit, or funding demand to plan cash. The useful forecast must match the decision's target and timing: a forecast of tomorrow's price level does not directly answer how uncertain next month's portfolio loss will be.
A forecast has an origin, a horizon and an information set
Write a point forecast as . The origin is when it is issued; the horizon is how far ahead it looks; the target is the specified quantity . Define the time unit as well: the next trading observation and the next calendar day need not coincide.
The information set contains what the forecaster could actually know at the origin. It includes publication delays and the data vintage then available. A revised economic release downloaded today may contain information unavailable when a historical forecast would have been issued. Letting that revision enter the historical fit creates look-ahead bias.
Forecasting can use past values of a time series, other observable predictors, or informed judgement. The defining discipline is the information boundary, rather than the complexity of the model.
Freeze the prediction before observing the outcome
Consider a synthetic index, measured in index points. At time , its observed value is . A persistence forecast carries the latest value forward, so the forecast for time is also . This simple rule is a useful benchmark for a level series; it is not automatically the appropriate benchmark for every target. Hyndman and Athanasopoulos describe this as the naïve method.
Later, time arrives and the actual index value is . With the convention actual minus forecast, the error is
The positive sign means the forecast was too low. Its squared error is squared index points. That is one observation's loss; mean squared error averages such losses over an evaluation set.
Original synthetic example in index points. The forecast is issued at time 0; the actual value at time 1 is shown only after it becomes observable. The dashed line is a persistence forecast, not an observed price path.
The original prediction stays in the record. Once becomes available, it can inform a new forecast from a later origin. Replacing the old forecast with the new information would destroy the test. A single miss also cannot establish whether the rule is skilful or useless.
A point is not the uncertainty around it
A point forecast compresses a forecast distribution into one number. Under squared-error loss and finite second moments, the conditional expectation is the optimal point forecast; under absolute-error loss, a conditional median is optimal. An estimated model need not recover either accurately.
A prediction interval describes a range for the future outcome under stated assumptions. It is different from a confidence interval for an estimated model coefficient. Future shocks, parameter uncertainty and changes in the underlying relationship can all matter. A flat persistence forecast therefore does not imply that the future index will stay flat or that uncertainty is zero. The forecaster's toolbox develops the distributional view; the membership lesson Forecasting from ARMA Models derives horizon-dependent forecasts and uncertainty (public preview available).
Judge the rule across later observations
In out-of-sample evaluation, each forecast must precede its target observation. Choose the target, horizon, benchmark and loss before inspecting final test results. Any model fitting, feature selection or data transformation must respect that same boundary. Repeatedly selecting the winner on the test period turns it into part of model development.
Compare competing rules on the same targets and dates. A more elaborate model earns support when it improves on the benchmark across a credible record, with allowance for sampling uncertainty and dependence between errors. Good fit to the observations used to estimate the model is a different achievement.
Finally, match the evaluation to the decision. Smaller forecast error does not by itself establish profitable trading after turnover and execution costs, or a better risk policy. The membership lesson Forecast Evaluation connects error measures to chronological tests and economic value (public preview available).
Sources
- Chris Brooks, Introductory Econometrics for Finance, 3rd ed., Cambridge University Press, 2014, §6.11.1–6.11.3, pp. 285–287; §6.11.8, pp. 292–294; §6.11.9, p. 295.
- Rob J. Hyndman and George Athanasopoulos, Forecasting: Principles and Practice, 3rd ed., Chapter 5: The forecaster's toolbox, especially §§5.2, 5.5, 5.8 and 5.10. Checked 26 October 2026.