Forecasting Baselines, Temporal Validation, and Backtesting

A demand planner faces a concrete problem: every Monday morning, using sales that are final only through Sunday night, they must forecast the next four weeks. The forecast is not a claim about a randomly selected future row. It is a claim about specific future dates, made from a specific information set, and it will be scored at several horizons.

Forecasting baselines are the simplest forecasts that respect time. The naive forecast repeats the last observed value. The seasonal-naive forecast repeats the last observed seasonal cycle. The canonical drift forecast continues the line through the first and last observations; fitting a separate trend is a different stated model. These methods are deliberately simple. Their job is to establish what a forecast must beat before we add exponential smoothing, ARIMA, gradient boosting, or neural networks. They also expose whether our validation is honest: a large improvement merits an information-availability audit, but it is not itself evidence of leakage.

This chapter treats forecasting as a sequence of forecast origins. At origin (o), we know the past up to (o) and must produce forecasts for (o+1,\ldots,o+H). The targets are future values (y_{o+1},\ldots,y_{o+H}), and none of them may enter the features, scaling, imputation, or model selection for that origin. We then move the origin forward and repeat the exercise. This is backtesting. It is the time-series analogue of cross-validation, but with an explicit arrow of time and an explicit forecast horizon.

We should keep this problem distinct from time-to-event analysis. In survival analysis, the outcome is a time to an event. Right-censoring records that the event has not occurred by the last observed follow-up time. In forecasting, the outcome is a value at a future date, such as demand next Tuesday. A missing future demand value is not a censored survival time; it is simply unavailable because the future has not happened. We can borrow careful thinking about information availability, but we should not blur the two targets.