Detrended Price Oscillator (DPO)

Summary

Detrended Price Oscillator: the price a half-cycle back, less the moving average that spans the cycle. Removing the average removes the trend, leaving the shorter oscillation that the trend was hiding.

It crosses zero as price crosses its own average, so peaks and troughs mark the cycle rather than the direction of the market. The distance between successive peaks estimates the cycle length, and the amplitude is in price units, so it is comparable across time only for one instrument.

Formula

Let t = optInTimePeriod / 2 + 1, an integer division, so a period and its odd successor share the same displacement.

DPO[i] = P[i - t] - SMA(P, optInTimePeriod)[i]

Notes

• The value is emitted at the bar whose moving average produced it. Charting packages usually draw it t bars to the left instead, which is a plotting convention rather than a different series; a caller wanting that view shifts outReal itself.
• A causal variant, P[i] - SMA(P, optInTimePeriod)[i - t], displaces the average instead of the price. It is a genuinely different series, not a re-indexing of this one, and is not implemented here.

Inputs

• inReal — Source price/value series, canonically the close

Outputs

• outReal — Detrended Price Oscillator value, in the units of the input

Parameters

Parameter	Type	Default	Accepted values	Description
optInTimePeriod	integer	20	2–100000	Number of bars spanned by the moving average being removed; the displacement is derived from it

Properties

Numerical Stability: Start-Independent

☐ Overlap Input
✅ Independent Y-Axis i
☐ Candlestick
☐ Can Output NaN or ±Inf
☐ Identity at Period 1

Implementation

TA-Lib Definition: dpo.c · dpo.yaml

Native	File
C	ta_DPO.c
Rust	dpo.rs
Java	Core_DPO.java

TA-Lib is also available for Python, R and more using a wrapper.

Aliases

Detrended Price Oscillator

See Also

SMA · MOM · APO

References

• Steven B. Achelis, Technical Analysis from A to Z, McGraw-Hill (p. 119)
• StockCharts ChartSchool: Detrended Price Oscillator