DPO — Detrended Price Oscillator

The close minus the simple average from n/2 + 1 bars ago — the common, non-centred form. Subtracting a lagged average removes the trend and leaves the cycle; the reading belongs to the current bar.

Signature

DPO(period, on=<source>)

Argument	Type	Required	Notes
period	int Param or literal	Yes	Cycle length to remove. Default 20, bounds 2–400.
on=	symbol, OHLCV field, or indicator	No	Source. Defaults to the trade symbol’s close.

Formula

$$ \text{DPO}t = C_t - \text{SMA}(C, n){t-(n/2+1)} $$

Warmup

period + int(period/2) + 1 bars — the lagged window has to be whole; 0 until then.

Reading the value

dpo.value
dpo > 0
dpo.crossed_above(0)

Example

class CycleTimer(Strategy):
    """Enter when the detrended cycle turns up from a trough."""
    period = Param(20, min=2, max=400)
    trade = Symbol()
    sizing = FixedCapital()

    def execute(self):
        dpo = DPO(self.period, on=self.trade)
        if dpo.crossed_above(0) and self.trade.is_flat:
            self.buy(self.trade, reason="Cycle up")
        if dpo.crossed_below(0) and self.trade.is_long:
            self.sell(self.trade, self.trade.position, reason="Cycle down")

Notes

• The non-centred construction most charting platforms ship by default (the lag is int(n/2) + 1). The centred textbook form — a past close minus the average centred on it — is not aligned with the current bar; this one is, at the cost of a lagged average.
• On a straight-line price the reading is the constant lag of the average, int(n/2) + 1 + (n − 1)/2 (20.5 for n = 20) — the trend the detrending removes.