Add Stochastic Oscillator implementation and validation tests

- Implemented Stochastic Oscillator (%K and %D) in Stoch.cs with streaming and batch processing capabilities. - Added validation tests for the Stochastic Oscillator in Stoch.Validation.Tests.cs, ensuring consistency with Skender.Stock.Indicators. - Created documentation for the Stochastic Oscillator in Stoch.md, detailing its mathematical formula, architecture, parameters, and common pitfalls. - Updated project file to include necessary numeric libraries for highest and lowest calculations.
2026-08-25 22:08:05 +00:00 · 2026-02-12 14:29:54 -08:00
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+# KDJ: Enhanced Stochastic Oscillator
+
+> "K leads, D confirms, J exaggerates — three perspectives on momentum."
+
+KDJ is an enhanced Stochastic Oscillator popular in Asian markets. It extends the classic Stochastic by adding a J line that amplifies divergence between K and D, providing earlier reversal signals. Uses Wilder's RMA (Exponential Moving Average with `α = 1/signal`) instead of SMA for smoother K and D lines.
+
+## Calculation
+
+1. Compute highest high and lowest low over the lookback period using monotonic deques.
+2. Calculate the Raw Stochastic Value (RSV).
+3. Smooth RSV with RMA to get K; smooth K with RMA to get D.
+4. Compute J as the amplified divergence.
+
+Formula:
+
+```
+RSV = 100 × (Close - LowestLow) / (HighestHigh - LowestLow)
+K = RMA(RSV, signal)    // α = 1/signal
+D = RMA(K, signal)      // α = 1/signal
+J = 3K - 2D
+```
+
+If the price range is zero, RSV defaults to `50.0` (neutral). K and D are clamped to `[0, 100]`. J is unbounded and can exceed 100 or go below 0.
+
+Exponential warmup compensators ensure accurate K and D values from the first bar, avoiding the typical initialization bias of recursive filters.
+
+## Interpretation
+
+- **K > D** → bullish momentum (K crosses above D = buy signal)
+- **K < D** → bearish momentum (K crosses below D = sell signal)
+- **J > 100** → strongly overbought, potential reversal down
+- **J < 0** → strongly oversold, potential reversal up
+- **K > 80** → overbought zone
+- **K < 20** → oversold zone
+
+## Parameters
+
+| Name | Type | Default | Range | Description |
+| :--- | :--- | :------ | :---- | :---------- |
+| `length` | `int` | `9` | `>0` | Lookback period for highest high / lowest low. |
+| `signal` | `int` | `3` | `>0` | RMA smoothing period for K and D lines. |
+
+## API
+
+```mermaid
+classDiagram
+    class Kdj {
+        +Name : string
+        +WarmupPeriod : int
+        +IsHot : bool
+        +K : TValue
+        +D : TValue
+        +Last : TValue (J line)
+        +Update(TBar input, bool isNew) TValue
+        +Update(TBarSeries source) (TSeries K, TSeries D, TSeries J)
+        +Prime(TBarSeries source) void
+        +Reset() void
+        +Batch(TBarSeries source, int length, int signal) (TSeries K, TSeries D, TSeries J)
+        +Batch(ReadOnlySpan~double~ high, low, close, Span~double~ kOut, dOut, jOut, int length, int signal) void
+        +Calculate(TBarSeries source, int length, int signal) ((TSeries K, TSeries D, TSeries J) Results, Kdj Indicator)
+    }
+```
+
+## Usage Example
+
+```csharp
+using QuanTAlib;
+
+// Initialize
+var kdj = new Kdj(length: 9, signal: 3);
+
+foreach (var bar in bars)
+{
+    kdj.Update(bar, isNew: true);
+
+    if (kdj.IsHot)
+    {
+        Console.WriteLine($"{bar.Time}: K={kdj.K.Value:F2} D={kdj.D.Value:F2} J={kdj.Last.Value:F2}");
+    }
+}
+```
+
+## Performance Profile
+
+| Metric | Score | Notes |
+| :--- | :--- | :--- |
+| **Throughput** | 9 | O(1) amortized via monotonic deques. |
+| **Allocations** | 0 | Zero allocations in hot path. |
+| **Complexity** | O(1) | Amortized constant time per update. |
+| **Accuracy** | 10 | Exact match with PineScript reference. Exponential warmup compensators. |
+| **Timeliness** | 8 | RMA smoothing provides faster response than SMA-based Stochastic. |
+| **Overshoot** | 7 | J line intentionally unbounded for early signals. |
+| **Smoothness** | 8 | Double RMA smoothing eliminates noise. |
+
+## Validation
+
+No direct TA-Lib/Tulip/Skender equivalent exists for KDJ with Wilder's RMA smoothing. Validation is performed against the PineScript reference and internal consistency checks:
+- Streaming vs Batch vs Span cross-mode consistency
+- Mathematical identity: J = 3K − 2D
+- K/D bounded in [0, 100]
+- Parameter sensitivity across multiple configurations
+
+## Sources
+
+- Chinese securities analysis (KDJ is a standard indicator on Chinese exchanges)
+- [PineScript reference](kdj.pine)