LSMA — Least Squares Moving Average

The endpoint of the rolling least-squares fit: where the regression line says price “should” be right now. Less lag than an SMA of the same length because a fitted line extrapolates the trend rather than averaging it away.

Signature

LSMA(period, on=<source>)

Argument	Type	Required	Notes
period	int Param or literal	Yes	Regression window. Default 25, bounds 2–400.
on=	symbol, OHLCV field, or indicator	No	Source. Defaults to the trade symbol’s close.

Formula

$$ \text{LSMA} = \text{intercept} + \text{slope},(n-1) $$

with slope and intercept from the ordinary least-squares fit of price on bar index.

Warmup

period bars; the raw close until the window fills.

Reading the value

lsma.value
lsma.crossed_above(sma)

Example

class LsmaCross(Strategy):
    """LSMA leads a same-length SMA — trade the spread between them."""
    period = Param(25, min=2, max=400)
    trade = Symbol()
    sizing = FixedCapital()

    def execute(self):
        lsma = LSMA(self.period, on=self.trade)
        sma = SMA(self.period, on=self.trade)
        if lsma.crossed_above(sma) and self.trade.is_flat:
            self.buy(self.trade, reason="LSMA over SMA")
        if lsma.crossed_below(sma) and self.trade.is_long:
            self.sell(self.trade, self.trade.position, reason="LSMA under SMA")

Notes

• Ordinary least squares; identical math to LinearRegression.fitted and LinearRegressionCurve — three names because members search for all three.
• Proven by an assert-via-trade run on SPY daily (matched a strategy-side OLS reference to 1e-3 on every bar; zero alarm trades).
• TSF is this line extended one bar further.