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.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](../stoch/Stoch.md), [StochRSI](../stochrsi/Stochrsi.md) | **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)

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

---

## 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:

```csharp
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