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docs: update category index files and fix indicator implementations (#58)

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lib/trends_IIR/_index.md
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Trend indicators based on Infinite Impulse Response (IIR) filters. Recursive architecture uses previous outputs to compute current values, enabling lower lag with fewer coefficients than equivalent FIR filters.
## Implementation Status
| Indicator | Full Name | Status | Description |
| :--- | :--- | :---: | :--- |
| [DEMA](dema/Dema.md) | Double Exponential MA |  | Reduces lag by applying double exponential smoothing, enhancing responsiveness while maintaining signal quality. |
| [DSMA](dsma/Dsma.md) | Deviation-Scaled MA |  | Adaptive IIR filter that adjusts smoothing factor based on market volatility, increasing responsiveness during high-deviation periods. |
| [EMA](ema/Ema.md) | Exponential MA |  | Applies exponentially decreasing weights to price data, balancing responsiveness and stability. |
| [FRAMA](frama/Frama.md) | Fractal Adaptive MA |  | Adapts smoothing based on fractal dimension analysis, minimizing lag in trends and maximizing smoothing in consolidation. |
| [HEMA](hema/Hema.md) | Hull Exponential MA |  | EMA-domain Hull analog using half-life timing and de-lagged EMA cascade. |
| [HTIT](htit/Htit.md) | Hilbert Transform Instantaneous Trend |  | Utilizes Hilbert Transform to isolate instantaneous trend component, providing zero-lag trendline with hybrid FIR-in-IIR design. |
| [JMA](jma/Jma.md) | Jurik MA |  | Adaptive filter achieving high noise reduction and low phase delay through multi-stage volatility normalization and dynamic parameter optimization. |
| [KAMA](kama/Kama.md) | Kaufman Adaptive MA |  | Automatically adjusts sensitivity based on market volatility using Efficiency Ratio, balancing responsiveness and stability. |
| [MAMA](mama/Mama.md) | MESA Adaptive MA |  | Applies Hilbert Transform for phase-based adaptation, using dual-line system (MAMA/FAMA) for cycle-sensitive smoothing. |
| [MGDI](mgdi/Mgdi.md) | McGinley Dynamic Indicator |  | Adjusts speed based on market volatility using dynamic factor, aiming to hug prices closely. |
| [MMA](mma/Mma.md) | Modified MA |  | Combines simple and weighted components, emphasizing central values for balanced smoothing. |
| [QEMA](qema/Qema.md) | Quad Exponential MA |  | Zero-lag filter with four cascaded EMAs using geometrically ramped alphas and minimum-energy weights for DC lag elimination. |
| [REMA](rema/Rema.md) | Regularized Exponential MA |  | Applies regularization to EMA using lambda parameter, balancing smoothing and momentum-based prediction. |
| [RGMA](rgma/Rgma.md) | Recursive Gaussian MA |  | Approximates Gaussian smoothing by recursively applying EMA filters multiple times (passes), controlled by adjusted period. |
| [RMA](rma/Rma.md) | wildeR MA (SMMA, MMA) |  | Wilder's smoothing average using specific alpha (1/period), designed for indicators like RSI and ATR. |
| [T3](t3/T3.md) | Tillson T3 MA |  | Six-stage EMA cascade with optimized coefficients based on volume factor for reduced lag and superior noise reduction. |
| [TEMA](tema/Tema.md) | Triple Exponential MA |  | Triple-cascade EMA architecture with optimized coefficients (3, -3, 1) for further lag reduction compared to DEMA. |
| [VAMA](vama/Vama.md) | Volatility Adjusted MA |  | Dynamically adjusts moving average length based on ATR volatility ratio, shortening during high volatility and lengthening during low volatility. |
| [VIDYA](vidya/Vidya.md) | Variable Index Dynamic Average |  | Adjusts smoothing factor based on market volatility using Volatility Index (ratio of short-term to long-term standard deviation). |
| [YZVAMA](yzvama/Yzvama.md) | Yang-Zhang Volatility Adjusted MA |  | Adjusts MA length based on percentile rank of short-term YZV, providing context-aware volatility adaptation for gap-prone markets. |
| [ZLEMA](zlema/Zlema.md) | Zero-Lag Exponential MA |  | Reduces lag by estimating future price based on current momentum, using dynamically calculated lag period. |
## Selection Guide
**For trend-following systems:** EMA provides baseline stability. DEMA/TEMA reduce lag at cost of increased overshoot. T3 offers best lag-to-smoothness ratio for most applications.
**For adaptive response:** KAMA adjusts to efficiency ratio (trend vs noise). VIDYA responds to volatility changes. FRAMA uses fractal dimension for market state detection. JMA combines all adaptive mechanisms into unified filter.
**For zero-lag requirements:** ZLEMA applies momentum-based lag compensation. HTIT uses Hilbert Transform for instantaneous trend. QEMA achieves DC lag elimination through cascaded architecture.
**For Wilder-family indicators:** RMA (SMMA) provides standard smoothing for RSI, ATR, ADX calculations.
## IIR Characteristics Comparison
| Filter | Lag (bars) | Smoothness | Overshoot | Adaptivity | Complexity |
| :--- | :---: | :---: | :---: | :---: | :---: |
| EMA | Period/2 | Medium | Low | None | O(1) |
| DEMA | Period/3 | Medium | Medium | None | O(1) |
| TEMA | Period/4 | Low | High | None | O(1) |
| T3 | Period/5 | High | Low | None | O(1) |
| ZLEMA | ~0 | Low | High | None | O(1) |
| KAMA | Variable | Variable | Low | Efficiency | O(n) |
| VIDYA | Variable | Variable | Low | Volatility | O(n) |
| FRAMA | Variable | Variable | Medium | Fractal | O(n) |
| JMA | ~1-2 | High | Very Low | Multi-factor | O(1) |
## Adaptive Filter Categories
| Category | Filters | Adaptation Mechanism | Best Application |
| :--- | :--- | :--- | :--- |
| **Fixed Alpha** | EMA, RMA, MMA | Constant smoothing factor | Stable trending markets |
| **Cascade** | DEMA, TEMA, T3, QEMA | Multiple EMA stages | Lag reduction priority |
| **Efficiency-Based** | KAMA | Direction vs noise ratio | Choppy/trending detection |
| **Volatility-Based** | VIDYA, VAMA, DSMA, YZVAMA | Standard deviation or ATR | Regime-change adaptation |
| **Fractal-Based** | FRAMA | Hurst exponent proxy | Range/trend detection |
| **Phase-Based** | MAMA, HTIT | Hilbert Transform | Cycle-sensitive smoothing |
| **Multi-Stage Adaptive** | JMA, MGDI | Combined mechanisms | Universal application |
## IIR vs FIR Design Principles
| Aspect | IIR Filters | FIR Filters |
| Indicator | Full Name | Description |
| :--- | :--- | :--- |
| **Memory** | O(1) state | O(period) buffer |
| **Computation** | 2-4 multiplications | period multiplications |
| **Stability** | Requires careful design | Always stable |
| **Phase Response** | Non-linear phase | Can be linear phase |
| **Lag Achievable** | Lower lag possible | Minimum lag = (period-1)/2 |
| **Adaptivity** | Natural (modify alpha) | Requires coefficient recalc |
| **SIMD Potential** | Limited (recursive) | High (parallel windows) |
## Alpha-Period Relationship
IIR filters use smoothing factor ± instead of explicit period. Conversion formulas:
| Formula | Expression | Use Case |
| :--- | :--- | :--- |
| Standard EMA | ± = 2/(period+1) | General purpose |
| Wilder (RMA) | ± = 1/period | RSI, ATR, ADX |
| Percentage | ± = percentage/100 | Direct control |
Effective period approximation: `period H 2/± - 1` for standard EMA weighting.
| [DEMA](lib/trends_IIR/dema/Dema.md) | Double Exponential MA | Reduces lag by applying double exponential smoothing, enhancing responsiveness while maintaining signal quality. |
| [DSMA](lib/trends_IIR/dsma/Dsma.md) | Deviation-Scaled MA | Adaptive IIR filter that adjusts smoothing factor based on market volatility, increasing responsiveness during high-deviation periods. |
| [EMA](lib/trends_IIR/ema/Ema.md) | Exponential MA | Applies exponentially decreasing weights to price data, balancing responsiveness and stability. |
| [FRAMA](lib/trends_IIR/frama/Frama.md) | Fractal Adaptive MA | Adapts smoothing based on fractal dimension analysis, minimizing lag in trends and maximizing smoothing in consolidation. |
| [HEMA](lib/trends_IIR/hema/Hema.md) | Hull Exponential MA | EMA-domain Hull analog using half-life timing and de-lagged EMA cascade. |
| [HTIT](lib/trends_IIR/htit/Htit.md) | Hilbert Transform Instantaneous Trend | Utilizes Hilbert Transform to isolate instantaneous trend component, providing zero-lag trendline with hybrid FIR-in-IIR design. |
| [JMA](lib/trends_IIR/jma/Jma.md) | Jurik MA | Adaptive filter achieving high noise reduction and low phase delay through multi-stage volatility normalization and dynamic parameter optimization. |
| [KAMA](lib/trends_IIR/kama/Kama.md) | Kaufman Adaptive MA | Automatically adjusts sensitivity based on market volatility using Efficiency Ratio, balancing responsiveness and stability. |
| [MAMA](lib/trends_IIR/mama/Mama.md) | MESA Adaptive MA | Applies Hilbert Transform for phase-based adaptation, using dual-line system (MAMA/FAMA) for cycle-sensitive smoothing. |
| [MGDI](lib/trends_IIR/mgdi/Mgdi.md) | McGinley Dynamic Indicator | Adjusts speed based on market volatility using dynamic factor, aiming to hug prices closely. |
| [MMA](lib/trends_IIR/mma/Mma.md) | Modified MA | Combines simple and weighted components, emphasizing central values for balanced smoothing. |
| [QEMA](lib/trends_IIR/qema/Qema.md) | Quad Exponential MA | Zero-lag filter with four cascaded EMAs using geometrically ramped alphas and minimum-energy weights for DC lag elimination. |
| [REMA](lib/trends_IIR/rema/Rema.md) | Regularized Exponential MA | Applies regularization to EMA using lambda parameter, balancing smoothing and momentum-based prediction. |
| [RGMA](lib/trends_IIR/rgma/Rgma.md) | Recursive Gaussian MA | Approximates Gaussian smoothing by recursively applying EMA filters multiple times (passes), controlled by adjusted period. |
| [RMA](lib/trends_IIR/rma/Rma.md) | wildeR MA | Wilder's smoothing average using specific alpha (1/period), designed for indicators like RSI and ATR. |
| [T3](lib/trends_IIR/t3/T3.md) | Tillson T3 MA | Six-stage EMA cascade with optimized coefficients based on volume factor for reduced lag and superior noise reduction. |
| [TEMA](lib/trends_IIR/tema/Tema.md) | Triple Exponential MA | Triple-cascade EMA architecture with optimized coefficients (3, -3, 1) for further lag reduction compared to DEMA. |
| [VAMA](lib/trends_IIR/vama/Vama.md) | Volatility Adjusted MA | Dynamically adjusts moving average length based on ATR volatility ratio, shortening during high volatility and lengthening during low volatility. |
| [VIDYA](lib/trends_IIR/vidya/Vidya.md) | Variable Index Dynamic Average | Adjusts smoothing factor based on market volatility using Volatility Index (ratio of short-term to long-term standard deviation). |
| [YZVAMA](lib/trends_IIR/yzvama/Yzvama.md) | Yang-Zhang Volatility Adjusted MA | Adjusts MA length based on percentile rank of short-term YZV, providing context-aware volatility adaptation for gap-prone markets. |
| [ZLEMA](lib/trends_IIR/zlema/Zlema.md) | Zero-Lag Exponential MA | Reduces lag by estimating future price based on current momentum, using dynamically calculated lag period. |
| LTMA | Linear Trend MA | Projects the linear trend of price data using linear regression, focusing on the endpoint of the trendline. |
| ZLDEMA | Zero-Lag Double Exponential MA | Hybrid dual-stage predictive architecture combining two ZLEMAs with optimized 1.5/0.5 coefficients for reduced lag and noise suppression. |
| ZLTEMA | Zero-Lag Triple Exponential MA | Advanced triple-cascade predictive architecture combining three ZLEMAs with optimized 2/2/1 coefficients for maximum lag reduction. |
lib/trends_IIR/kama/Kama.cs
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@@ -303,17 +303,8 @@ public sealed class Kama : AbstractBase
// oldest: when full, oldest is at bufferIdx (the next write position)
// Note: bufferIdx has already been advanced, so current value is at (bufferIdx - 1 + bufSize) % bufSize
double change;
if (count == bufSize)
{
// When full, oldest is at bufferIdx (next write position)
change = Math.Abs(val - buffer[bufferIdx]);
}
else
{
// When not full, oldest is at index 0
change = Math.Abs(val - buffer[0]);
}
// When full, oldest is at bufferIdx (next write position); when not full, oldest is at index 0
double change = Math.Abs(val - buffer[count == bufSize ? bufferIdx : 0]);
double er = (volatilitySum > 1e-10) ? change / volatilitySum : 0.0;
if (er > 1.0) er = 1.0;
@@ -338,4 +329,4 @@ public sealed class Kama : AbstractBase
_p_state = _state;
Last = default;
}
}
}