What this calculator does
Time Series and Forecasting is Module 17 of Analysis Studio, and it sits in the subscription set. It provides:
- Decomposition of a series into trend, seasonal, and remainder parts
- Trend tests that respect the ordering of the observations
- Automatic ETS and ARIMA forecasting, with the candidate set compared on a holdout the models never saw during fitting
Every forecast is scored against a seasonal naive benchmark, the forecast that simply repeats the last observed season. A model that cannot beat that benchmark on the holdout is reported as failing to beat it, because a forecast that loses to the naive rule has not earned its complexity.
Promotion, stated with its date: through March 31, 2027, this module runs free on screen, like every module. Downloads and Copy Results stay with the subscription throughout. After the promotion, the module returns to the subscription set at $299 per year.
The method, in plain terms
A time series is not a sample: each observation arrives knowing the ones before it, so the methods here work with that dependence rather than assuming it away. Decomposition separates the level and trend from the repeating seasonal pattern so each can be read on its own. The ETS family builds forecasts from weighted averages of the past, with recent observations weighted more heavily; the weights are the smoothing parameters. The ARIMA family models the correlation between an observation and its predecessors directly. The module fits both families, holds back the most recent stretch of the series, and keeps the model that forecast the holdout best, with the seasonal naive result printed beside it as the bar to clear.
Worked example
Twelve monthly counts: 112, 118, 121, 119, 126, 131, 129, 135, 138, 136, 142, 147. A simple exponential smoothing fit with smoothing weight 0.5, the form that tracks a level without a stated trend, walks the level through the series and ends at:
- Final level: 142.8
- Forecast for the next month: 142.8
- One-step errors across the series, squared and summed: 421.8
The reading is in the construction: each month, the level moves halfway from its previous value toward the new observation, so the level trails a rising series by design. On a series with this steady a climb, the module's automatic search weighs trend-carrying forms against this one on the holdout, and the worked numbers here are the level-only yardstick those forms have to beat.
When the calculator fits, and when it does not
It fits when:
- Observations arrive in time order at regular intervals: monthly sales, weekly counts, daily traffic.
- The question is a forecast with an honest account of its accuracy, scored on data the model did not fit.
- The series carries a seasonal pattern, and the forecast needs to state it rather than average over it.
It does not fit when:
- The intervals are irregular and the gaps carry meaning. The module reads regular series; event-time data needs a different apparatus.
- The series is very short. A handful of points cannot support model selection, and the module says so rather than fitting a search over nothing.
- The question is causal, what a change in one series does to another. That is a regression question with time-aware errors, not a univariate forecast.
Run it
Module 17: Time Series and ForecastingOpen in Analysis Studio →Load your data in time order, pick the series and its frequency, and read the decomposition and the holdout scores before the forecast table.
Questions
What does the seasonal naive benchmark prove? That the chosen model earned its place. The seasonal naive forecast repeats the last season and costs nothing; if a fitted model cannot beat it on data the model never saw, the model is decoration. The module prints the comparison either way.
Why hold out the end of the series? Because a model can fit the data it was built on and still forecast badly. The holdout is the only honest test available: fit on the earlier stretch, forecast the later one, and compare with what actually happened.
ETS or ARIMA: which does the module choose? Whichever forecasts the holdout better, from the candidate set each family offers. The two families often land close together on well-behaved series; the holdout score, not a preference for one family, makes the call.
How far ahead can I forecast? As far as the interface allows, with the interval widening as it should. A forecast twelve months out from twelve months of data is mostly interval; the module prints that width rather than a falsely precise line.
My series has a strong weekly or yearly pattern. Is that handled? Yes, when the frequency is stated. The seasonal component is estimated at the stated period, the decomposition shows it separately, and the seasonal naive benchmark uses the same period, so the comparison is fair.