QuanTAlib/lib/oscillators/dstoch/Dstoch.md

DSTOCH: Double Stochastic (Bressert DSS)

Apply the Stochastic formula twice — once to price, once to the result — and the oscillator sharpens from a gentle hill into a decisive cliff.

Property	Value
Category	Oscillator
Inputs	High, Low, Close
Parameters	period (default 21)
Outputs	Single series (Dstoch)
Output range	[0, 100]
Warmup	period bars
PineScript	dstoch.pine

• 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 that is more responsive than standard Stochastic.
• Similar: Stoch, StochRSI | Complementary: ADX for trend confirmation | Trading note: Overbought above 80, oversold below 20; sharper transitions than single Stochastic.
• No external validation libraries implement DSS Bressert. Validated through self-consistency and behavioral testing.

DSTOCH applies the Stochastic normalization formula to price, then applies it again to the normalized result with EMA smoothing in between. This double application sharpens the oscillator's transitions, making overbought/oversold signals more decisive while remaining bounded to [0, 100].

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}

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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.

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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.

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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

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References

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