The loop in four steps
| Step | When | What to record or compute |
|---|---|---|
| 1. Log | When the forecast is made | Date made, date it is for, point forecast, interval and its coverage (80% or 95%), who or what made it (assistant, model, version), one line of reasoning |
| 2. Score | When the outcome is known | Outcome; error = outcome − forecast; inside or outside the interval; for yes-or-no questions, the Brier score |
| 3. Compare | Every review | The same scores for the benchmarks below, on the same periods |
| 4. Retire | After enough outcomes to judge | Drop or rework any forecast that does not beat the best benchmark |
The forecast score calculator does steps 2 and 3 for a pasted log: MAE, RMSE, MAPE, bias, interval coverage, the Winkler score, the Brier score and a comparison with the naive forecast.
The benchmarks to beat
Hyndman and Athanasopoulos use four simple methods as benchmarks throughout Forecasting: Principles and Practice, calling them "extremely simple and surprisingly effective" (section 5.2, checked 13 November 2026).
| Benchmark | Forecast for every future period | The book's note |
|---|---|---|
| Mean | The average of all past values | Every future forecast is the same number |
| Naive | The last observed value | Works "remarkably well for many economic and financial time series" |
| Seasonal naive | The last observed value from the same season, such as the same month last year | Useful for highly seasonal data |
| Drift | The last value plus the average change per period so far, times the number of periods ahead | The same as drawing a line from the first to the last observation and extending it |
How the benchmarks did in the book's examples
The same four methods win in different places. The book scores them on two real series, forecasting periods the methods had not seen.
| Example | Method | RMSE | MAE | MAPE | MASE |
|---|---|---|---|---|---|
| Australian beer production, quarterly, 2008 to 2010 | Mean | 38.45 | 34.83 | 8.28 | 2.44 |
| Naive | 62.69 | 57.40 | 14.18 | 4.01 | |
| Seasonal naive | 14.31 | 13.40 | 3.17 | 0.94 | |
| Drift | 64.90 | 58.88 | 14.58 | 4.12 | |
| Google closing stock price, January 2016 | Mean | 118.03 | 116.95 | 16.24 | 16.41 |
| Naive | 43.43 | 40.38 | 5.67 | 5.67 | |
| Drift | 53.07 | 49.82 | 6.99 | 6.99 |
Source: Forecasting: Principles and Practice, section 5.8, checked 13 November 2026. Lower is better; the best method in each example is in bold. For the seasonal beer series, repeating last year's quarter beat every other benchmark on all four measures. For the stock price, repeating yesterday's close did. A predictive assistant forecasting either series has to beat that number to be worth reading.
Score genuine forecasts only
Score forecasts made before the outcome was known. The book is direct about it: the accuracy of forecasts "can only be determined by considering how well a model performs on new data that were not used when fitting the model" (section 5.8). A back-test that lets the model see the period it is predicting will look better than live use. If you need to test before going live, use time series cross-validation: forecast each period using only the data before it, then average the errors (section 5.10).
How many outcomes before you judge
Interval calibration needs many outcomes: after 10 forecasts at 80%, anything from 6 to 10 inside is within 2 standard deviations of the expected 8, so even a perfect log looks noisy. The uncertainty guide explains the arithmetic. For yes-or-no forecasts, compare the Brier score with the score from always forecasting the base rate, which the calculator reports.
Sources
Checked 13 November 2026:
- Hyndman, R. J. and Athanasopoulos, G., Forecasting: Principles and Practice, 3rd ed., OTexts: 5.2 Some simple forecasting methods, 5.8 Evaluating point forecast accuracy, 5.10 Time series cross-validation
Next step
Paste last quarter's forecasts and outcomes into the forecast score calculator and read the relative MAE first: below 1 means the forecasts beat the naive one.
Frequently asked questions
- What is a naive forecast?
- A forecast that repeats the last observed value. Hyndman and Athanasopoulos note it works remarkably well for many economic and financial time series, which makes it the first benchmark any model should beat.
- Which benchmark should a forecast beat?
- The best of the mean, naive, seasonal naive and drift methods on your own data. For seasonal data that is often seasonal naive; in Forecasting Principles and Practice's beer example it had a MASE of 0.94 against 2.44 to 4.12 for the other three.