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124 lines
3.6 KiB
Markdown
124 lines
3.6 KiB
Markdown
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# DSTOCH — Double Stochastic (Bressert DSS)
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## Overview
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**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.
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| Property | Value |
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| :--------- | :-------------- |
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| Category | Oscillator |
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| Output | Single (DSS) |
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| Range | [0, 100] |
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| Default | period = 21 |
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| Input | TBar (HLC) |
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| Hot after | period bars |
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**Source:** [Dstoch.cs](Dstoch.cs) · [PineScript](dstoch.pine)
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---
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## Formula
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### Stage 1: Raw %K
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$$
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\text{rawK}_t = \begin{cases}
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100 \cdot \frac{C_t - LL_t}{HH_t - LL_t} & \text{if } HH_t \neq LL_t \\
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0 & \text{otherwise}
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\end{cases}
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$$
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where $HH_t$ and $LL_t$ are the highest high and lowest low over the last $n$ bars.
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### Stage 1: EMA Smoothing
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$$
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\text{smoothK}_t = \alpha \cdot \text{rawK}_t + (1 - \alpha) \cdot \text{smoothK}_{t-1}
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$$
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where $\alpha = \frac{2}{n + 1}$.
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### Stage 2: Stochastic of smoothK
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$$
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\text{dsRaw}_t = \begin{cases}
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100 \cdot \frac{\text{smoothK}_t - \min(\text{smoothK}, n)}{\max(\text{smoothK}, n) - \min(\text{smoothK}, n)} & \text{if range} > 0 \\
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0 & \text{otherwise}
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\end{cases}
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$$
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### Stage 2: EMA Smoothing (Final Output)
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$$
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\text{DSS}_t = \alpha \cdot \text{dsRaw}_t + (1 - \alpha) \cdot \text{DSS}_{t-1}
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$$
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---
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## Interpretation
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| Zone | Meaning |
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| :-------- | :------------------------------------- |
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| DSS > 80 | Overbought — potential bearish reversal|
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| DSS < 20 | Oversold — potential bullish reversal |
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| Cross 50↑ | Bullish momentum shift |
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| Cross 50↓ | Bearish momentum shift |
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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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---
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## Implementation Details
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### 1. MonotonicDeque Streaming (Stage 1)
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Two `MonotonicDeque` instances provide O(1) amortized min/max tracking for HH/LL:
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- **Max deque**: decreasing order of highs; front is always the window maximum.
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- **Min deque**: increasing order of lows; front is always the window minimum.
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- **Circular buffers** (`_hBuf`, `_lBuf`): store raw H/L values for deque rebuild on bar correction.
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### 2. MonotonicDeque Streaming (Stage 2)
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A second pair of `MonotonicDeque` instances tracks `smoothK` values:
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- **`_skMaxDeque`**: highest smoothK over the window.
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- **`_skMinDeque`**: lowest smoothK over the window.
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- **`_skBuf`**: circular buffer for smoothK values.
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### 3. EMA Smoothing
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Both EMA stages use `Math.FusedMultiplyAdd` for optimal precision:
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```csharp
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smoothK = Math.FusedMultiplyAdd(prev_smoothK, decay, alpha * rawK);
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```
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### 4. Bar Correction
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On `isNew=false`, all four deques are rebuilt from their circular buffers via `RebuildMax`/`RebuildMin`, and the scalar state is restored from `_ps`.
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### 5. Batch Path
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The batch implementation uses `Highest.Batch` / `Lowest.Batch` for both stages, with `stackalloc` for ≤ 256 elements and `ArrayPool` beyond.
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---
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## Complexity Analysis
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| Operation | Complexity |
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| :--------------------- | :------------- |
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| Per-update (amortized) | O(1) |
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| Per-update (worst) | O(n) |
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| Bar correction | O(n) × 4 deques|
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| Batch (N bars) | O(N) |
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| Memory (streaming) | O(n) × 3 buffers + 4 deques |
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---
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## References
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- Bressert, W. (1998). *The Power of Oscillator/Cycle Combinations*
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- TradingView: DSS Bressert indicator
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- Investopedia: Double Smoothed Stochastic
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