AutoCorrelation — Auto-Correlation

Correlation of returns with their own lag. Positive means momentum persists bar to bar; negative means the series reverses itself — the most direct statistical test of whether a mean-reversion or a trend rule is the right shape for this instrument.

Signature

AutoCorrelation(period, lag, on=<source>)

Argument	Type	Required	Notes
period	int Param or literal	Yes	Return window. Default 60, bounds 3–400.
lag	int Param or literal	Yes	Lag in bars. Default 1, bounds 1–100.
on=	symbol, OHLCV field, or indicator	No	Source. Defaults to the trade symbol’s close.

Formula

$$ \rho_k = \frac{\sum_{i} (r_i - \bar{r})(r_{i+k} - \bar{r})}{\sum_i (r_i - \bar{r})^2} $$

on log returns.

Warmup

period + 1 bars; 0 until then.

Reading the value

ac.value
ac.value < -0.1     # the series is reverting
ac.value > 0.1      # the series is trending

Example

class RegimeSwitch(Strategy):
    """Only fade extremes when returns are actually negatively autocorrelated."""
    trade = Symbol()
    sizing = FixedCapital()

    def execute(self):
        ac = AutoCorrelation(60, 1, on=self.trade)
        z = ZScore(20, on=self.trade)
        if ac.value < -0.1 and z.value < -2 and self.trade.is_flat:
            self.buy(self.trade, reason=f"Reverting regime, z {z.value:.2f}")
        if z.value > 0 and self.trade.is_long:
            self.sell(self.trade, self.trade.position, reason="Mean reached")

Notes

• Proven by an assert-via-trade run on SPY daily (stayed inside ±1 on every bar of a 140-bar run; zero alarm trades).
• Daily equity autocorrelation is small and unstable — a reading of ±0.1 is meaningful, ±0.5 would be extraordinary and worth double-checking before trusting.