# Tilson T3 Moving Average

The T3 moving average was developed by Tom Tilson.  It is designed to be smoother and more responsive than traditional moving averages, but like a moving linear regression, it can overshoot price or the indicator to which it is applied.

It combines triple, quadruple, quintuple and sextuple exponential moving averages into a single moving average.

Custom PCF Formula
 `-(f ^ 3) * XAVG(XAVG(XAVG(XAVG(XAVG(XAVGCx, x), x), x), x), x) + 3 * ((f ^ 2) + (f ^ 3)) * XAVG(XAVG(XAVG(XAVG(XAVGCx, x), x), x), x) - (6 * (f ^ 2) + 3 * (f + (f ^ 3))) * XAVG(XAVG(XAVG(XAVGCx, x), x), x) + (1 + 3 * f + (f ^ 3) + 3 * (f ^ 2)) * XAVG(XAVG(XAVGCx, x), x)` `x`=Period, `f`=Volume Facter (normally .7 or .618)

Where x is the period and must be an integer.

Where f is the volume factor (which is normally 0.7 or 0.618).

### Examples

A 3 period Tilson T3 with a Volume Factor of .7 could be written as follows.

`-(.7 ^ 3) * XAVG(XAVG(XAVG(XAVG(XAVG(XAVGC3, 3), 3), 3), 3), 3) + 3 * ((.7 ^ 2) + (.7 ^ 3)) * XAVG(XAVG(XAVG(XAVG(XAVGC3, 3), 3), 3), 3) - (6 * (.7 ^ 2) + 3 * (.7 + (.7 ^ 3))) * XAVG(XAVG(XAVG(XAVGC3, 3), 3), 3) + (1 + 3 * .7 + (.7 ^ 3) + 3 * (.7 ^ 2)) * XAVG(XAVG(XAVGC3, 3), 3)`

An 8 period Tilson T3 with a Volume Factor of .618 could be written as follows.

`-(.618 ^ 3) * XAVG(XAVG(XAVG(XAVG(XAVG(XAVGC8, 8), 8), 8), 8), 8) + 3 * ((.618 ^ 2) + (.618 ^ 3)) * XAVG(XAVG(XAVG(XAVG(XAVGC8, 8), 8), 8), 8) - (6 * (.618 ^ 2) + 3 * (.618 + (.618 ^ 3))) * XAVG(XAVG(XAVG(XAVGC8, 8), 8), 8) + (1 + 3 * .618 + (.618 ^ 3) + 3 * (.618 ^ 2)) * XAVG(XAVG(XAVGC8, 8), 8)`   