Derivative Oscillator (DOSC)

Summary

Derivative Oscillator: Wilder's RSI, smoothed by two exponential averages in series, with a simple average of that smoothed line subtracted from it. Constance Brown's reading is that the RSI's own swings are too noisy to time with, so she smooths it twice and then plots the distance from its own average as a histogram — MACD's histogram construction, applied to a smoothed RSI rather than to price. The result is in RSI points, centred on zero: crossings of the zero line mark the turn, and the height measures how far the smoothed RSI has run from its mean.

Formula

RSI = RSI(inReal, timePeriod) (Wilder, SMA-seeded)

S1 = EMA(RSI, firstPeriod)

DS = EMA(S1, secondPeriod)

DOSC = DS - SMA(DS, signalPeriod)

Notes

• Every stage is a function TA-Lib already ships, and the output is identical, bit for bit, to TA_RSI followed by two TA_EMA calls, a TA_SMA and a TA_SUB. That chain takes five calls and their intermediate buffers; this computes it in one pass without materialising them.
• Each exponential average is seeded with a simple average of its own first inputs, the same seeding TA-Lib's EMA uses, and the second seeds on what the first publishes. TA_SetUnstablePeriod on either TA_FUNC_UNST_RSI or TA_FUNC_UNST_EMA discards more of that warm-up, and the EMA setting counts twice because there are two exponential stages. Implementations seeding each stage from a single first sample differ over the transient and agree once it decays.
• The degenerate reading is whatever TA_RSI answers when neither a gain nor a loss has been seen since the seed. Some other implementations answer 100 there and will disagree over that stretch.
• The periods are independent: no ordering between the two smoothing periods is required or checked. Swapping them changes the outputs, most at the start: each average is seeded on its own inputs, and that difference decays to rounding level. A signal period of 1 would make the output identically zero, so the minimum is 2.

Inputs

• inReal — Input series, usually the close

Outputs

• outReal — Derivative Oscillator, in RSI points, centred on zero

Parameters

Parameter	Type	Default	Accepted values	Description
optInTimePeriod	integer	14	2–100000	Period of the RSI
optInFirstPeriod	integer	5	2–100000	Period of the first smoothing, applied to the RSI
optInSecondPeriod	integer	3	2–100000	Period of the second smoothing, applied to the first
optInSignalPeriod	integer	9	2–100000	Period of the simple average subtracted from the smoothed line

Properties

Numerical Stability: Initial Unstable Period — Inherited from EMA and RSI, which DOSC computes internally; tunable via EMA and RSI's unstable period.

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

Implementation

TA-Lib Definition: dosc.c · dosc.yaml

Native	File
C	ta_DOSC.c
Rust	dosc.rs
Java	Core_DOSC.java
C#	Core_DOSC.cs

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

Aliases

derivative oscillator

See Also

RSI · STOCHRSI · MACD · AC

References

• Constance M. Brown, "The Derivative Oscillator: A New Approach for an Old Problem", MTA Journal (Market Technicians Association), Issue 42, Winter 1993-Spring 1994, pp. 45-55 and 61