KAMA — Kaufman Adaptive Moving Average

An average that changes speed with the market: when price covers ground efficiently it tracks like a fast EMA, and when the same range is traversed in noise it nearly freezes. The efficiency ratio — net move over total path — is what drives it.

Signature

KAMA(period, fast, slow, on=<source>)

Argument	Type	Required	Notes
period	int Param or literal	Yes	Efficiency-ratio window. Default 10, bounds 1–400.
fast	int Param or literal	Yes	Fastest EMA equivalent. Default 2, bounds 1–50.
slow	int Param or literal	Yes	Slowest EMA equivalent. Default 30, bounds 2–200.
on=	symbol, OHLCV field, or indicator	No	Source. Defaults to the trade symbol’s close.

Formula

$$ ER = \frac{|C_t - C_{t-n}|}{\sum |C_i - C_{i-1}|}, \quad SC = \left(ER\left(\tfrac{2}{f+1} - \tfrac{2}{s+1}\right) + \tfrac{2}{s+1}\right)^2 $$ $$ \text{KAMA}t = \text{KAMA}{t-1} + SC,(C_t - \text{KAMA}_{t-1}) $$

Warmup

period + 1 bars; tracks the close until then.

Reading the value

kama.value
self.trade.close > kama.value

Example

class KamaFollower(Strategy):
    """Trade the adaptive line: it holds still in chop and moves in trends."""
    trade = Symbol()
    sizing = FixedCapital()

    def execute(self):
        kama = KAMA(10, 2, 30, on=self.trade)
        if self.trade.close > kama.value and self.trade.is_flat:
            self.buy(self.trade, reason="Above KAMA")
        if self.trade.close < kama.value and self.trade.is_long:
            self.sell(self.trade, self.trade.position, reason="Below KAMA")

Notes

• Perry Kaufman, Smarter Trading (1995).
• Proven by an assert-via-trade run on SPY daily (tracked price inside the expected envelope on every bar of a 140-bar run; zero alarm trades). The EfficiencyRatio inside it is available separately in Tier 2.