T3 is an excellent data-fitting technique by Tim Tillson (cf. "Smoothing Techniques For More Accurate Signals" in Technical Analysis of Stocks and Commodities - January 1998)
N is the Exponential Moving Average Period a is the amplification percentage of the filter's response to price movement (0 < a < 1)
e1 = N-days EMA of Close Prices e2 = N-days EMA of e1 e3 = N-days EMA of e2 e4 = N-days EMA of e3 e5 = N-days EMA of e4 e6 = N-days EMA of e5
c1 = (-a)^3 c2 = 3 * a^2 c3 = - 6 * a^2 - 3 * a - 3 * a^3 c4 = 1 + 3 * a + a^3 + 3 * a^2
T3 = c1 * e6 + c2 * e5 + c3 * e4 + c4 * e3