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This indicator plots the moving average described in the January, 1998 issue

of S&C, p.57, "Smoothing Techniques for More Accurate Signals", by Tim Tillson.

This indicator plots T3 moving average presented in Figure 4 in the article.

T3 indicator is a moving average which is calculated according to formula:

T3(n) = GD ( GD ( GD (n))),

where GD - generalized DEMA ( Double EMA ) and calculating according to this:

GD (n,v) = EMA (n) * (1+v)-EMA( EMA (n)) * v,

where "v" is volume factor, which determines how hot the moving average’s response

to linear trends will be. The author advises to use v=0.7.

When v = 0, GD = EMA , and when v = 1, GD = DEMA . In between, GD is a less aggressive

version of DEMA . By using a value for v less than1, trader cure the multiple DEMA

overshoot problem but at the cost of accepting some additional phase delay.

In filter theory terminology, T3 is a six-pole nonlinear Kalman filter. Kalman

filters are ones that use the error — in this case, (time series - EMA (n)) —

to correct themselves. In the realm of technical analysis , these are called adaptive

moving averages; they track the time series more aggres-sively when it is making large

moves. Tim Tillson is a software project manager at Hewlett-Packard, with degrees in

mathematics and computer science. He has privately traded options and equities for 15 years.

of S&C, p.57, "Smoothing Techniques for More Accurate Signals", by Tim Tillson.

This indicator plots T3 moving average presented in Figure 4 in the article.

T3 indicator is a moving average which is calculated according to formula:

T3(n) = GD ( GD ( GD (n))),

where GD - generalized DEMA ( Double EMA ) and calculating according to this:

GD (n,v) = EMA (n) * (1+v)-EMA( EMA (n)) * v,

where "v" is volume factor, which determines how hot the moving average’s response

to linear trends will be. The author advises to use v=0.7.

When v = 0, GD = EMA , and when v = 1, GD = DEMA . In between, GD is a less aggressive

version of DEMA . By using a value for v less than1, trader cure the multiple DEMA

overshoot problem but at the cost of accepting some additional phase delay.

In filter theory terminology, T3 is a six-pole nonlinear Kalman filter. Kalman

filters are ones that use the error — in this case, (time series - EMA (n)) —

to correct themselves. In the realm of technical analysis , these are called adaptive

moving averages; they track the time series more aggres-sively when it is making large

moves. Tim Tillson is a software project manager at Hewlett-Packard, with degrees in

mathematics and computer science. He has privately traded options and equities for 15 years.

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//////////////////////////////////////////////////////////// // Copyright by HPotter v1.0 21/05/2014 // This indicator plots the moving average described in the January, 1998 issue // of S&C, p.57, "Smoothing Techniques for More Accurate Signals", by Tim Tillson. // This indicator plots T3 moving average presented in Figure 4 in the article. // T3 indicator is a moving average which is calculated according to formula: // T3(n) = GD(GD(GD(n))), // where GD - generalized DEMA (Double EMA) and calculating according to this: // GD(n,v) = EMA(n) * (1+v)-EMA(EMA(n)) * v, // where "v" is volume factor, which determines how hot the moving average’s response // to linear trends will be. The author advises to use v=0.7. // When v = 0, GD = EMA, and when v = 1, GD = DEMA. In between, GD is a less aggressive // version of DEMA. By using a value for v less than1, trader cure the multiple DEMA // overshoot problem but at the cost of accepting some additional phase delay. // In filter theory terminology, T3 is a six-pole nonlinear Kalman filter. Kalman // filters are ones that use the error — in this case, (time series - EMA(n)) — // to correct themselves. In the realm of technical analysis, these are called adaptive // moving averages; they track the time series more aggres-sively when it is making large // moves. Tim Tillson is a software project manager at Hewlett-Packard, with degrees in // mathematics and computer science. He has privately traded options and equities for 15 years. //////////////////////////////////////////////////////////// study(title="T3 Averages", shorttitle="T3", overlay = true) Length = input(5, minval=1) xPrice = close xe1 = ema(xPrice, Length) xe2 = ema(xe1, Length) xe3 = ema(xe2, Length) xe4 = ema(xe3, Length) xe5 = ema(xe4, Length) xe6 = ema(xe5, Length) b = 0.7 c1 = -b*b*b c2 = 3*b*b+3*b*b*b c3 = -6*b*b-3*b-3*b*b*b c4 = 1+3*b+b*b*b+3*b*b nT3Average = c1 * xe6 + c2 * xe5 + c3 * xe4 + c4 * xe3 plot(nT3Average, color=blue, title="T3")