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### 8.9 Kaufman Adaptive Moving Average

The Kaufman adaptive moving average (KAMA) by Perry J. Kaufman (http://www.perrykaufman.com) is an exponential style average (see Exponential Moving Average) but with a smoothing that varies according to recent data. In a steadily progressing move the latest prices are tracked closely, but when going back and forward with little direction the latest prices are given only small weights.

The smoothing factor is determined from a given past N days closes (default 10). The net change (up or down) over that time is expressed as a fraction of the total daily changes (up and down). This is called the “efficiency ratio”. If every day goes in the same direction then the two amounts are the same and the ratio is 1. But in the usual case where prices backtrack to some extent then the net will be smaller than the total. The ratio is 0 if no net change at all.

```     abs (close[today] - close[N days ago])
ER = --------------------------------------
Sum     abs (close - close[prev])
past N days
```

The ER is rescaled to between 0.0645 and 0.666 and then squared to give an alpha factor for the EMA of between 0.444 and 0.00416. This corresponds to EMA periods from a fast 3.5 days to a very slow 479.5 days.

```alpha = (ER * 0.6015 + 0.0645) ^ 2
```

An exponential moving average of prices is then taken, using each alpha value calculated.

```KAMA = alpha * close + (1-alpha) * KAMA[prev]
```

These alpha values can be viewed directly with “KAMA alpha” in the lower indicator window (a low priority option, near the end of the lists). High values show where KAMA is tracking recent prices closely, low values show where it’s responding only slowly.