Forecast Lab: Time-Series Backtest & Forecast Ranges

Forecast Lab is a three-step wizard for extrapolating one equally spaced series — monthly, quarterly or daily numbers — into the near future. It detects a seasonal period, plots the autocorrelation function, races six forecast models in a rolling backtest, and returns an h-step forecast with 95% bands. The history alone drives the answer, and every readout is reproducible.

Updated 2026-10-01Reviewed by CalcX Editorial Team5 sources4 min read

How to forecast a series

Load the series.Paste numbers separated by spaces, commas or newlines, click a demo, or pull a vector or table column from the data workspace; eight finite points is the floor.
Read the health check.The season line names the best period m and its strength (below 0.3 means no clear seasonality), and the ACF chart places the first lags against the dashed ±1.96/√n white-noise band.
Run the model race.The rolling backtest holds out the last points, refits on each prefix and ranks one-step-ahead MAE across naive, drift, SMA, EWMA, linear trend and (when a season period is set) Holt-Winters; MAPE and RMSE sit beside it, with one line on the winner.
Forecast.Set the horizon h (1 to n), optionally force a model, edit period m, and switch additive or multiplicative seasonality (multiplicative appears only when every value is positive). The cards report the next-step value, its 95% interval and the residual σ; h above n/2 raises an extrapolation warning.
Hand the numbers on.Publish a card, or send the forecast table and points to the data workspace or the graphing calculator.

Worked readouts

Every figure comes from the two demo buttons; the same paste reproduces them.

Step	Input	Readout
Check	Quarterly revenue, 20 points	Season m = 4, strength 0.97; ACF lag 1 0.6531 against the ±0.4383 white-noise band
Race	same series, hold = 4	Holt-Winters MAE 1.1876 (MAPE 0.771%, RMSE 1.3131); linear trend 8.9719; SMA 9.5; EWMA 10.908; naive 11.75; drift 11.998
Forecast	winner, h = 4	Next step 174.318, 95% interval 171.23 … 177.41, residual σ 1.5756; later steps 157.470501, 153.500074, 170.755617
Check	Monthly actives, 12 points	Season m = 2, strength 0.644; the race puts linear 0.26427 just ahead of Holt-Winters 0.27457
Forecast	linear, h = 2	28.9197 then 30.9022; step-1 interval 28.473 … 29.366, residual σ 0.22785

The race line reads "MAE 1.188 vs runner-up 8.972"; the four quarterly means add to 656.044109 against 599 for the latest actual year.

Six models in one race

Naive repeats the last value, drift adds the average slope, SMA averages a window, EWMA smooths exponentially, linear trend fits an OLS line, and Holt-Winters tracks level, trend and season. The Holt-Winters parameters α, β and γ are grid-searched over five values each — the best of 125 combinations, not an MLE. Intervals are the RMS of in-sample one-step residuals, widened by √k: σ = 1.5756 gives half-widths of 3.088 at step 1, 6.176 at step 4 and 10.24 at step 11. The race is decided on the held-out tail.

Assumptions and limits

The answer inherits the series and the settings.: Points are taken as equally spaced; intervals are residual normal approximations ±1.96·σ·√k, not analytic intervals, and the √k widening is a random-walk rule. A constant series ties every model at MAE 0 (naive wins by display order), and a horizon above half the history is flagged but still computed.
What it does not do:: no ARIMA, no explanatory variable, no fuller seasonality test, no structural-break handling — the history is extrapolated mechanically. For summaries and hypothesis tests use Statistics; for power, control charts and life data use Applied Statistics.

The season period gates the race

On the monthly demo the detector finds m = 2 (strength 0.644) even though the button says trend only, so Holt-Winters is admitted and loses by a hair: 0.26427 for linear against 0.27457. Type 4 into Season m and the same data crowns Holt-Winters at 0.19618. Add a thirteenth month at 28.5 and the automatic race flips as well: Holt-Winters 0.28117 against linear 0.36741. On the quarterly demo the winning 1.1876 requires m = 4; with no usable period the best MAE is 8.9719. The period also sets the default horizon (4 quarters here, 2 months monthly). Record it, or the model changes underneath the forecast.

Where it fits

Planning the next four quarters

The revenue demo answers the wizard's own question: next quarter 174.318, a four-quarter total of 656.044109 against 599 for the latest actual year, and a near-end 95% interval of 171.23 … 177.41.

Sizing capacity from a monthly trend

The actives demo rises from 28.9197 to 30.9022 in two months and reaches 50.7274 by month 12; the step-1 interval 28.473 … 29.366 is tight enough for staffing, while the far steps carry half-widths from 0.4466 to 1.547 and an h > n/2 warning.

Vetting a forecast someone handed you

If naive or drift beats the proposed model, the number needs more evidence; the ACF chart shows whether structure exceeds the white-noise band. Keep the series in the data workspace.

References

Hyndman, R.J. & Athanasopoulos, G., Forecasting: Principles and Practice, 3rd ed., otexts.com （访问日期：2026-10-01）— backtesting, holdout error and forecast evaluation.
Hyndman, R.J. & Athanasopoulos, G., Forecasting: Principles and Practice, 3rd ed., Chapter 8, otexts.com （访问日期：2026-10-01）— exponential smoothing, Holt-Winters and additive vs multiplicative seasonality.
NIST/SEMATECH, e-Handbook of Statistical Methods, §6.4.3 What is Exponential Smoothing?, itl.nist.gov （访问日期：2026-10-01）— smoothing constants and one-step prediction error.
Wikipedia, Autocorrelation, en.wikipedia.org （访问日期：2026-10-01）— ACF, lag structure and white-noise bands.
Wikipedia, Prediction interval, en.wikipedia.org （访问日期：2026-10-01）— the difference between prediction and confidence intervals.