Tillson T3: six smoothings arranged to cancel their own lag

What it measures

T3 applies exponential smoothing six times and then combines the results with coefficients derived from a volume factor, arranged so that the lag of the smoothing partly cancels itself.

The result is unusually smooth for how closely it tracks price — smoother than a triple EMA and less laggy than a simple average of comparable smoothness.

The volume factor has nothing to do with traded volume. It is a coefficient controlling how aggressively the lag cancellation is applied.

That naming causes real confusion. Nothing about T3 reads volume at all — the factor is a smoothing coefficient, and an implementation that fed it actual volume would be computing something else entirely.

How it is calculated

These are the steps Basis performs, verified against the published definition.

1. 1

   Apply an exponential average to price, then to that result, and so on to a sixth generation.

2. 2

   Compute four coefficients from the volume factor.

3. 3

   Combine the third through sixth generations using those coefficients.

Settings

A period of eight with a volume factor of 0.7 is the common setting. Because the smoothing compounds six times, the effective lookback is far longer than the period implies — expect an eight-period T3 to behave like a much longer average, and treat the volume factor rather than the period as the responsiveness dial.

How to read it

• Treat it as a smooth trend line. Its slope is reliable in a way a short average’s is not.
• It still overshoots at sharp reversals, because the lag cancellation extrapolates in the same way a zero-lag construction does.
• It is a good input for other calculations precisely because it is smooth without being slow.
• Because six generations of smoothing are combined, a T3 needs a substantial warm-up before its values mean anything — far more bars than the period suggests.

Where it misleads

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