Why is seasonal-naive the first baseline you fit for a 48-hour electricity-load forecast?

## What the two naive rules are Two baselines cover most forecasting work, and they are not interchangeable. - **Naive, or last-value:** the forecast for every future step is the most recent observation. `y_hat[t+h] = y[t]` for all `h`. This is the optimal forecast when the series behaves like a random walk, where the best guess about tomorrow genuinely is today. - **Seasonal-naive:** the forecast for a future step is the observation from the same phase of the previous cycle. With a seasonal period `m`, `y_hat[t+h] = y[t+h-m]`. For hourly data with a weekly period, `m = 168`, so next Tuesday 09:00 is predicted by last Tuesday 09:00. For daily data with a weekly period, `m = 7`. Neither has parameters, neither is fitted, and both can be produced in one pass over the history. ## Why a baseline comes first An error number on its own is uninterpretable. An error of 4.2 could be outstanding or embarrassing depending on how variable the series is and how much of that variability is trivially predictable. The baseline converts an absolute number into a statement about **skill**: how much of the error the model removes relative to a rule that requires no learning. That is the sentence that survives being repeated to a stakeholder — "we cut the error 18% below repeating last week" — where "our error is 4.2" is not. There are three further reasons the baseline goes first rather than last: 1. **It catches broken pipelines early.** If your trained model is *worse* than repeating last week, something is usually wrong with the framing — a misaligned label, a shuffled ordering, a target the features cannot see — and you learn it in an hour instead of a week. 2. **It is a deployable fallback.** Seasonal-naive is what the system serves when the model is unavailable, so knowing its error is knowing the cost of degraded mode. 3. **It disciplines the scope.** If the naive rule is close to the model after weeks of work, the honest recommendation may be not to run a model at all. ## Choosing the right naive rule The choice follows the structure of the series. - **Strong repeating cycle at the sampling frequency** — hourly electricity load, daily retail footfall, hourly ride demand — seasonal-naive with the dominant period. For load, the weekly period usually beats the daily one because it gets weekends right without a special case. - **No cycle, dominated by persistence** — a slowly drifting sensor reading, a price-like level — last-value naive. Seasonal-naive here just injects a week-old noise draw and will be clearly worse. - **Cycle plus visible trend** — seasonal-naive with drift, which adds the average change per period observed over the history to the seasonal value. ## Making the comparison fair A baseline comparison is only informative if the baseline is subject to exactly the same constraints as the model: - **Same forecast origin.** If the model must produce all 48 hours at 06:00, the baseline must too. A baseline that quietly uses observations from after the origin is not a baseline, it is a leak, and it will make your model look worse than it is. - **Same holdout period.** Comparing a model on one stretch of history to a baseline on another compares seasons, not methods. - **Same error metric, computed identically.** Whatever measure you have chosen for the project, apply it unchanged to both, over the same rows. ## Strengthening the baseline before you accept it Before concluding the model wins, make the baseline as strong as it cheaply can be. The average of the same hour across the last four weeks reduces the variance of relying on one week-old observation. A holiday override — do not use last Tuesday when this Tuesday is a public holiday — removes the baseline's most embarrassing failures. If the model's margin survives against that stronger reference, it is real. ## Reading the result A large margin over seasonal-naive means the model captures structure the cycle alone does not: weather sensitivity, holiday effects, trend. A small margin invites a closer look — is the gain concentrated in a few unusual hours, which may be exactly the hours that matter operationally, or is it uniform and marginal? And a negative margin is not a reason to tune harder; it is a reason to re-examine the framing.