A quiet, active, quiet sequence with changing signs
Use these 12 hypothetical daily simple returns as a small arithmetic example. The dates are consecutive trading observations, and the percentages describe the same asset on the same sampling basis. The middle four observations have larger magnitudes even though their signs change. Twelve observations illustrate a calculation; they are not enough to establish a reliable market model.
- Across all 12 observations, the mean signed return is zero and the mean squared decimal return is 0.0044 / 12. Its square root is 1.9149% per observation, which does not reveal where the active interval occurred.
- Under an explicit zero-mean assumption, a four-observation rolling root mean square is 1% after observation 4, 3% after observation 8 and 1% after observation 12. These are window endpoints, not forecasts made before those windows.
- The quiet and active labels here were assigned after seeing the sequence. A tradable filter must instead set its threshold in advance and use only observations available at the decision time.
| Observations | Returns in time order | Absolute returns | Descriptive interval |
|---|---|---|---|
| 1 to 4 | -1%, -1%, -1%, +1% | 1%, 1%, 1%, 1% | Quiet |
| 5 to 8 | +3%, -3%, -3%, +3% | 3%, 3%, 3%, 3% | Active |
| 9 to 12 | +1%, +1%, +1%, -1% | 1%, 1%, 1%, 1% | Quiet |