QuanTAlib/lib/oscillators/dstoch/Dstoch.md

DSTOCH — Double Stochastic (Bressert DSS)

Overview

DSTOCH (Double Stochastic / DSS Bressert) applies the Stochastic oscillator formula twice with EMA smoothing between stages, producing a momentum indicator bounded between 0 and 100. Developed by Walter Bressert, it is more responsive than standard Stochastic while remaining bounded.

Property	Value
Category	Oscillator
Output	Single (DSS)
Range	[0, 100]
Default	period = 21
Input	TBar (HLC)
Hot after	period bars

Source: Dstoch.cs · PineScript

---

Formula

Stage 1: Raw %K

\text{rawK}_t = \begin{cases}
100 \cdot \frac{C_t - LL_t}{HH_t - LL_t} & \text{if } HH_t \neq LL_t \\
0 & \text{otherwise}
\end{cases}

where HH_t and LL_t are the highest high and lowest low over the last n bars.

Stage 1: EMA Smoothing

\text{smoothK}_t = \alpha \cdot \text{rawK}_t + (1 - \alpha) \cdot \text{smoothK}_{t-1}

where \alpha = \frac{2}{n + 1}.

Stage 2: Stochastic of smoothK

\text{dsRaw}_t = \begin{cases}
100 \cdot \frac{\text{smoothK}_t - \min(\text{smoothK}, n)}{\max(\text{smoothK}, n) - \min(\text{smoothK}, n)} & \text{if range} > 0 \\
0 & \text{otherwise}
\end{cases}

Stage 2: EMA Smoothing (Final Output)

\text{DSS}_t = \alpha \cdot \text{dsRaw}_t + (1 - \alpha) \cdot \text{DSS}_{t-1}

---

Interpretation

Zone	Meaning
DSS > 80	Overbought — potential bearish reversal
DSS < 20	Oversold — potential bullish reversal
Cross 50↑	Bullish momentum shift
Cross 50↓	Bearish momentum shift

The double application of the Stochastic formula makes DSTOCH more sensitive to short-term price changes than the standard Stochastic oscillator.

---

Implementation Details

1. MonotonicDeque Streaming (Stage 1)

Two MonotonicDeque instances provide O(1) amortized min/max tracking for HH/LL:

• Max deque: decreasing order of highs; front is always the window maximum.
• Min deque: increasing order of lows; front is always the window minimum.
• Circular buffers (_hBuf, _lBuf): store raw H/L values for deque rebuild on bar correction.

2. MonotonicDeque Streaming (Stage 2)

A second pair of MonotonicDeque instances tracks smoothK values:

• _skMaxDeque: highest smoothK over the window.
• _skMinDeque: lowest smoothK over the window.
• _skBuf: circular buffer for smoothK values.

3. EMA Smoothing

Both EMA stages use Math.FusedMultiplyAdd for optimal precision:

smoothK = Math.FusedMultiplyAdd(prev_smoothK, decay, alpha * rawK);

4. Bar Correction

On isNew=false, all four deques are rebuilt from their circular buffers via RebuildMax/RebuildMin, and the scalar state is restored from _ps.

5. Batch Path

The batch implementation uses Highest.Batch / Lowest.Batch for both stages, with stackalloc for ≤ 256 elements and ArrayPool beyond.

---

Complexity Analysis

Operation	Complexity
Per-update (amortized)	O(1)
Per-update (worst)	O(n)
Bar correction	O(n) × 4 deques
Batch (N bars)	O(N)
Memory (streaming)	O(n) × 3 buffers + 4 deques

---

References

• Bressert, W. (1998). The Power of Oscillator/Cycle Combinations
• TradingView: DSS Bressert indicator
• Investopedia: Double Smoothed Stochastic