Forecasting as Supervised Learning

P7.forecasting.04 · Audience: guest, it-ml, language-pro · Prerequisites: Baselines You Must Beat, Supervised Learning Algorithms

ARIMA, Gently Backtesting & Anomaly Detection

Everything so far has been purpose-built forecasting machinery — smoothing dials and ARIMA dials. This module shows a different move entirely: reshape the series so that the whole Traditional ML toolbox from P5 applies to it. One table transformation turns "forecast the future" into "predict a target column", and suddenly every regressor you already know is a forecaster. The trick is powerful, widely used — and it re-arms the exact leakage trap this pillar opened with.

Step 1 / 4 — The pivot: lags become columns

Slide a window along the series and stack what it sees. Each position contributes one row: the previous values become feature columns — lag features — and the next value becomes the target. Take the tiny series [10, 12, 13, 15, 14, 16] with two lags:

y(t−2)	y(t−1)	target y(t)
10	12	13
12	13	15
13	15	14
15	14	16

That is the entire trick. The result looks exactly like the tabular data of the Traditional ML pillar: feature columns, a numeric target, one row per example. Forecasting has become regression on lags — predict y(t) from y(t−1) and y(t−2). To forecast tomorrow, build the feature row from the latest observed values and ask the model for its prediction.

🗣️ From a linguist's perspective: You have seen this window before

This is the n-gram move from language modelling: predict the next word from the previous few. A bigram model is exactly a one-lag predictor over words; the lag table above is a "trigram model" over numbers. In both worlds the window pretends only the recent past matters — and in both worlds that pretence is what makes the problem tractable at all.

✅ Key takeaways

The lag transformation slides a window along the series and stacks rows: previous values become feature columns, the next value becomes the target — forecasting becomes regression on lags.
From the table onward, the modelling is P5's: same algorithms, same fitting discipline. The time axis adds the feature vocabulary — lags, trailing rolling statistics, calendar columns, covariates — under one rule: nothing computed at or after the target's time.
Shuffled cross-validation on a lag table lies by construction: test rows carry training-set values inside their own lag features. Honest splits keep all training data strictly before all test data.
Supervised forecasting wins on covariates, learning across many related series, and nonlinear interactions; tree models cannot extrapolate a trend beyond the training range.
The bar is unchanged from module 01: beat the baselines on MASE, on temporally honest splits — a great CV score that loses to seasonal naive is still negative work.

Next: P7.forecasting.05 — Backtesting & Anomaly Detection

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