SMMA — Smoothed Moving Average

Wilder’s smoothed moving average (RMA): the recursive average ATR and RSI are built from. Equivalent to an EMA with alpha = 1/n instead of 2/(n+1) — about twice as slow as an EMA of the same period.

Signature

SMMA(period, on=<source>)

Argument	Type	Required	Notes
period	int Param or literal	Yes	Smoothing length. Default 14, bounds 1–400.
on=	symbol, OHLCV field, or indicator	No	Source. Defaults to the trade symbol’s close.

Formula

$$ \text{SMMA}t = \text{SMMA}{t-1} + \frac{C_t - \text{SMMA}_{t-1}}{n} $$

seeded with the simple average of the first n values.

Warmup

period bars to seed. During the lead-in it returns the running average of the bars seen so far; from bar n on, the recursion.

Reading the value

smma.value
smma.crossed_above(other)
price > smma.value

Example

class SmmaTrend(Strategy):
    """The Wilder-average trend filter: long above, flat below."""
    period = Param(50, min=1, max=400)
    trade = Symbol()
    sizing = FixedCapital()

    def execute(self):
        smma = SMMA(self.period, on=self.trade)
        if self.trade.close > smma.value and self.trade.is_flat:
            self.buy(self.trade, reason="Above SMMA")
        if self.trade.close < smma.value and self.trade.is_long:
            self.sell(self.trade, self.trade.position, reason="Below SMMA")

Variants

SMMA(14, on=tr)                  # ATR is exactly this, applied to true range
SMMA(20, on=self.trade.high)     # smoothed highs

Notes

• Wilder, New Concepts in Technical Trading Systems (1978).
• Seeded with the simple average of the first n bars (Wilder’s own convention). Because the recursion carries state, values in the first ~3n bars of a chart differ slightly from an implementation seeded elsewhere; they converge geometrically.
• Proven by an assert-via-trade run on SPY daily (converged to a strategy-side Wilder recursion within 0.01 after 60 bars; zero alarm trades).
• A different recipe from pandas_ta’s smma(7), not a different scale: measured on a 300-bar tape ours stays about 1.2 % away and never converges to it, because the construction (window offset, seed, weight normalisation) is its own.