Tillson T3 Average

Published by Tim Tillson in "Better Moving Averages" (Stocks & Commodities, January 1998), T3 runs price through six cascaded exponential moving averages of the same period N - e1 through e6, each one an EMA of the previous - and then combines three of those passes with weighted coefficients derived from a single "volume factor" b: c1 = -b^3 c2 = 3b^2 + 3b^3 c3 = -6b^2 - 3b - 3b^3 c4 = 1 + 3b + b^3 + 3b^2 T3 = c1*e6 + c2*e5 + c3*e4 + c4*e3 Plotting e6 alone (a plain sextuple EMA) would produce an extremely smooth but extremely laggy line. T3's coefficients instead blend e3 through e6 so that most of the six-pass smoothing's noise reduction is kept while a meaningful share of lag is cancelled back out - this is the specific trick that makes T3 worth using over just chaining EMAs by hand and picking one pass to plot. The volume factor b controls where T3 sits between those two extremes: b near 0 pulls the blend toward tracking price closely (behaving close to a single EMA), while b near 1 pulls in more of the deeper, smoother passes. Tillson's own suggested default is 0.7, used here. Notes and limitations - Recursive across all six passes: the very first computable bar has no prior value for any of them and is seeded by setting all six passes equal to that bar's own price, the standard EMA cold start. - Only one seed bar of extra history is needed, but a genuinely clean six-pass cascade still takes a number of bars after the seed to settle - the earliest plotted values will be closer to the seed price than a fully warmed-up T3 value would be. - Does not repaint - each closed bar's value is fixed once computed.

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Tags: Moving Average · Volume · MT4 Indicator · MQL4 Source Code

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