Ehlers Elegant Oscillator

The Elegant Oscillator is John Ehlers' answer to the question of how to turn momentum into a bounded, smooth swing with very little lag. It starts from the change in the source over two bars, which is centred on zero and ignores the slow trend.

That change is divided by its root mean square over the last RMS Length bars (50 by default), so it is measured in standard deviations of recent movement and means the same in quiet and busy markets. The inverse Fisher transform, (exp(2x) - 1) / (exp(2x) + 1), then squeezes it into the range -1 to 1: small values pass almost unchanged, while large ones are soft-clipped toward the edges rather than cut off.

Last, a two-pole super smoother with its cutoff at Band Edge bars (20 by default) smooths the result. The oscillator is drawn as a line around a dashed zero line.

The line swings between about -1 and 1. Readings near the edges mean the recent move is large compared with the window's usual movement, and because the inverse Fisher transform flattens the extremes, the line tends to sit near an edge briefly and then turn decisively. A turn down from near 1 or up from near -1 is the usual reversal reading, and a crossing of zero shows momentum changing side.

The smoother adds a little lag, so the turns come a few bars after the price turn. In a strong steady trend the line can hold near one edge for a long time, which is a sign of strength rather than of a reversal.