QuanTAlib/lib/oscillators/kdj/Kdj.md

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

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

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