Step response: earlier arrival, then overshoot
Start both EMA stages at 100 on bar 0, equivalent to a constant prior price of 100. On bar 1 the source jumps to 110 and stays there. Every stage has length 9. Define arrival as the first completed bar at or above 109, which is 90% of the 10-unit change. DEMA arrives on bar 4; EMA arrives on bar 11. These are threshold measurements for this input, not universal lag values.
- The exact DEMA peak is 111.073741824 on bars 9 and 10. Overshoot relative to the step size is (111.073741824 − 110) / 10 × 100 = 10.73741824%. This is not a return.
- A close crossing above its average happens on bar 1 for both lines. Faster threshold arrival therefore does not guarantee an earlier price-cross entry.
- Price never falls in this experiment, yet DEMA eventually sits above it. A subsequent price-below-DEMA condition can reflect the filter correction rather than a new decline in price.
| Bar | Source | EMA (9) | EMA of EMA (9) | DEMA (9) |
|---|---|---|---|---|
| 0 | 100 | 100.000000 | 100.000000 | 100.000000 |
| 1 | 110 | 102.000000 | 100.400000 | 103.600000 |
| 4 | 110 | 105.904000 | 102.627200 | 109.180800 |
| 5 | 110 | 106.723200 | 103.446400 | 110.000000 |
| 9 | 110 | 108.657823 | 106.241904 | 111.073742 |
| 10 | 110 | 108.926258 | 106.778775 | 111.073742 |
| 11 | 110 | 109.141007 | 107.251221 | 111.030792 |