HMA — Hull Moving Average

Alan Hull’s low-lag average: extrapolate the difference between a half-period and full-period weighted average, then smooth the result over √n. Turns almost with price — and overshoots at sharp reversals, which is the trade, not a bug.

Signature

HMA(period, on=<source>)

Argument	Type	Required	Notes
period	int Param or literal	Yes	Length. Default 9, bounds 2–400.
on=	symbol, OHLCV field, or indicator	No	Source. Defaults to the trade symbol’s close.

Formula

$$ \text{raw} = 2,\text{WMA}(C, n/2) - \text{WMA}(C, n), \quad \text{HMA} = \text{WMA}(\text{raw}, \lfloor\sqrt{n}\rfloor) $$

WMA weights the window linearly, newest heaviest.

Warmup

n + √n bars; the value tracks the raw close during the lead-in.

Reading the value

hma.value
price > hma.value
hma.crossed_above(slow)

Example

class HullTrend(Strategy):
    """Ride the Hull MA's direction."""
    period = Param(21, min=2, max=400)
    trade = Symbol()
    sizing = FixedCapital()

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

Notes

• Alan Hull (2005). Integer truncation on n/2 and √n follows the common convention.
• Proven by an assert-via-trade run on SPY daily (matched an independent strategy-side WMA chain exactly on every bar; zero alarm trades).
• Lower lag than DEMA/TEMA at the same period, at the cost of larger overshoot.