wickra/docs/wiki/indicators/momentum/Indicator-Dpo.md

DPO

Detrended Price Oscillator — removes the trend from price by comparing a shifted past price to the moving average, exposing the underlying cycle.

Quick reference

Field	Value
Family	Momentum
Sub-category	Unbounded oscillators
Input type	f64 (single close)
Output type	f64
Output range	unbounded around zero (price-difference scale)
Default parameters	period = 20 (Python)
Warmup period	max(period, period / 2 + 2)
Interpretation	Detrended price; peak-to-peak spacing reveals the cycle length.

Formula

shift = period / 2 + 1
DPO_t = price_{t − shift} − SMA(period)_t

A normal oscillator compares price to a current average and therefore still carries the trend. DPO instead subtracts the average from a price taken period / 2 + 1 bars back — roughly half a cycle. The dominant trend cancels, and what is left swings around zero with the same period as the price's shorter cycles, so the distance between DPO peaks reads off the cycle length directly.

DPO is not a momentum or signal indicator: by construction it is shifted into the past and is not meant to track the latest bar.

Parameters

Name	Type	Default	Valid range	Description
period	usize	20 (Python)	>= 1	SMA length; also sets the look-back shift = period / 2 + 1. 0 errors with Error::PeriodZero.

The Python binding defaults period to 20. The derived shift is exposed as a read-only property.

Inputs / Outputs

From crates/wickra-core/src/indicators/dpo.rs:

impl Indicator for Dpo {
    type Input = f64;
    type Output = f64;
    // update(&mut self, input: f64) -> Option<f64>
}

A single f64 close in, an Option<f64> out. Python maps this to float | None / numpy.ndarray (NaN warmup); Node to number | null / Array<number> (NaN warmup).

Warmup

warmup_period() == max(period, period / 2 + 2). The output needs both a full period-bar SMA window and a price shift bars back; the indicator becomes ready once the rolling window holds enough bars for both. For the usual period >= 4 this simplifies to period.

Edge cases

• Constant series. On a flat series the shifted price equals the SMA, so DPO is 0 (constant_series_yields_zero pins this).
• NaN / infinity inputs. Non-finite inputs are silently dropped; the window is not advanced.
• Reset. dpo.reset() clears the window and the rolling sum.

Examples

Rust

use wickra::{BatchExt, Indicator, Dpo};

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let mut dpo = Dpo::new(4)?;
    let out: Vec<Option<f64>> = dpo.batch(&[1.0, 2.0, 3.0, 4.0, 5.0, 6.0]);
    println!("{:?}", out);
    println!("shift = {}, warmup_period = {}", dpo.shift(), dpo.warmup_period());
    Ok(())
}

Output:

[None, None, None, Some(-1.5), Some(-1.5), Some(-1.5)]
shift = 3, warmup_period = 4

DPO(4) has shift = 3. At input 4 the SMA of [1,2,3,4] is 2.5 and the price 3 bars back is 1, giving 1 − 2.5 = −1.5. On a pure ramp the detrended value is constant. This matches the reference_values test in crates/wickra-core/src/indicators/dpo.rs.

Python

import numpy as np
import wickra as ta

dpo = ta.DPO(4)
print(dpo.batch(np.array([1.0, 2.0, 3.0, 4.0, 5.0, 6.0])))

Output:

[ nan  nan  nan -1.5 -1.5 -1.5]

Node

const ta = require('wickra');
const dpo = new ta.DPO(4);
console.log(dpo.batch([1, 2, 3, 4, 5, 6]));

Output:

[ NaN, NaN, NaN, -1.5, -1.5, -1.5 ]

Interpretation

Dpo is a cycle-measurement tool, not a trading trigger. Read it for the spacing of its peaks and troughs: regular spacing reveals the dominant cycle length, which you can then feed back into the periods of other indicators. Crossing zero is not a signal — because the series is shifted into the past, the latest DPO value does not correspond to the latest bar.

Common pitfalls

• Trading the zero cross. DPO is detrended and time-shifted; its latest value is historical. Use it to size cycles, not to time entries.
• Reading it as momentum. It is a detrended price, not a rate of change — see Roc or Mom for momentum.

References

The Detrended Price Oscillator is a standard cycle-analysis study; the period / 2 + 1 look-back shift used here matches the common definition (StockCharts, TA-Lib-compatible implementations).

See also

• Indicator-Sma.md — the moving average DPO detrends against.
• Indicator-Roc.md — momentum, the indicator DPO is often confused with.
• Indicators-Overview.md — the full taxonomy.