TEMA — Triple EMA

Mulloy’s second-order lag correction: three chained EMAs combined so both first- and second-order lag mostly cancel. Faster than DEMA, noisier again.

Signature

TEMA(period, on=<source>)

Argument	Type	Required	Notes
period	int Param or literal	Yes	EMA length. Default 20, bounds 1–400.
on=	symbol, OHLCV field, or indicator	No	Source. Defaults to the trade symbol’s close.

Formula

$$ \text{TEMA} = 3e_1 - 3e_2 + e_3, \quad e_1 = \text{EMA}(C,n),\ e_2 = \text{EMA}(e_1,n),\ e_3 = \text{EMA}(e_2,n) $$

Warmup

The chain seeds from the first value and converges over roughly 3n bars.

Reading the value

tema.value
tema.crossed_above(other)

Example

class TemaPullback(Strategy):
    """Buy the close reclaiming a fast TEMA in an uptrend."""
    fast = Param(9, min=1, max=400)
    slow = Param(50, min=1, max=400)
    trade = Symbol()
    sizing = FixedCapital()

    def execute(self):
        f = TEMA(self.fast, on=self.trade)
        s = SMA(self.slow, on=self.trade)
        if self.trade.close > s.value and self.trade.close > f.value and self.trade.is_flat:
            self.buy(self.trade, reason="Reclaimed TEMA in uptrend")
        if self.trade.close < s.value and self.trade.is_long:
            self.sell(self.trade, self.trade.position, reason="Trend gone")

Notes

• Patrick Mulloy, TASC (1994).
• Proven by an assert-via-trade run on SPY daily (converged to an independent strategy-side triple-EMA replication within 0.05 after 40 bars; zero alarm trades).
• Not “an EMA of an EMA of an EMA” — the combination is what removes the lag.
• The recursion seeds from the first bar rather than from a warm-up window, so early values are not comparable with TA-Lib TEMA(20), which seeds from an average of the first n; measured on a 300-bar tape the two agree to 1e-6 from bar 138 onward.