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https://github.com/mihakralj/QuanTAlib.git
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feat: Add Blackman Window Moving Average (BLMA) implementation and documentation
This commit is contained in:
Miha Kralj
@@ -14,6 +14,7 @@
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- [ALMA - Arnaud Legoux MA](../lib/trends/alma/Alma.md)
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- [BESSEL - Bessel Filter](../lib/trends/bessel/Bessel.md)
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- [BILATERAL - Bilateral Filter](../lib/trends/bilateral/Bilateral.md)
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- [BLMA - Blackman Window MA](../lib/trends/blma/Blma.md)
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- [CONV - Convolution](../lib/trends/conv/Conv.md)
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- [DEMA - Double Exponential MA](../lib/trends/dema/Dema.md)
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- [DWMA - Double Weighted MA](../lib/trends/dwma/Dwma.md)
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@@ -68,6 +68,7 @@ These measure the spread of data points around the mean.
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- [**ALMA**](../lib/trends/alma/Alma.md) - Arnaud Legoux MA
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- [**BESSEL**](../lib/trends/bessel/Bessel.md) - Bessel Filter
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- [**BILATERAL**](../lib/trends/bilateral/Bilateral.md) - Bilateral Filter
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- [**BLMA**](../lib/trends/blma/Blma.md) - Blackman Window MA
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- [**CONV**](../lib/trends/conv/Conv.md) - Convolution MA
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- [**DEMA**](../lib/trends/dema/Dema.md) - Double Exponential MA
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- [**DWMA**](../lib/trends/dwma/Dwma.md) - Double Weighted MA
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@@ -1,17 +1,18 @@
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# Trend Indicators Comparison
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Scale 1–10 where **10 = better** for every column.
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Scale 1–10 where **10 = better** for every column. Detailed evaluation criteria at the bottom of this doc.
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- Accuracy: preserves large-scale structure WITHOUT warping/projection artifacts
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- Timeliness: low lag / fast response
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- Overshoot Control: 10 = no overshoot / no ringing
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- Smoothness: noise suppression / stability
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- **Accuracy**: Preserve true movement structure (major trends and turning points) without distortion or artificial patterns.
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- **Timeliness**: Minimal lag. Fast response to genuine movement changes and reversals.
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- O**vershoot Control**: Remain within min/max of input, avoid generating artificial over-reaching levels and false threshold triggers.
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- **Smoothness**: Noise suppression. Stable output with smooth derivatives (no erratic velocity/acceleration).
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| Indicator | Accuracy | Timeliness | Overshoot Control | Smoothness | Notes (revised) |
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| :--- | :---: | :---: | :---: | :---: | :--- |
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| **ALMA** | 8 | 7 | 10 | 8 | Positive-weight FIR; accurate-ish but still a lag tradeoff. |
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| **BESSEL** | 9 | 7 | 9 | 8 | Strong shape/phase preservation; step response is well-behaved. |
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| **BILATERAL** | 7 | 6 | 10 | 8 | Edge-preserving; excellent in ranging markets, variable smoothing by design. |
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| **BLMA** | 7 | 3 | 10 | 10 | Standard DSP window; superior noise suppression but significant lag. |
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| **DEMA** | 4 | 9 | 3 | 6 | Lag-canceling subtraction ⇒ structure distortion + overshoot risk. |
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| **DWMA** | 7 | 2 | 10 | 10 | Ultra-smooth, but smears structure heavily (lag dominates). |
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| **EMA** | 8 | 6 | 10 | 8 | Convex IIR (monotone) ⇒ faithful & stable, moderate lag. |
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+1
-1
@@ -30,7 +30,7 @@
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| **Beta Coefficient** | Beta | BETA | - | Beta | - |
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| **Bias** | Bias | - | - | - | - |
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| **Bilateral Filter** | [Bilateral](../lib/trends/bilateral/Bilateral.md) | - | - | - | - |
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| **Blackman Window MA** | Blma | - | - | - | - |
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| **Blackman Window MA** | [Blma](../lib/trends/blma/Blma.md) | - | - | - | - |
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| **Bollinger %B** | Bbb | - | - | - | ❔ |
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| **Bollinger Band Squeeze** | Bbs | - | - | - | - |
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| **Bollinger Band Width** | Bbw | - | - | - | ❔ |
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+1
-1
@@ -55,7 +55,7 @@
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| BETA | Beta Coefficient | Statistics |
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| BIAS | Bias | Statistics |
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| [BILATERAL](trends/bilateral/Bilateral.md) | Bilateral Filter | Trends |
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| BLMA | Blackman Window MA | Trends |
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| [BLMA](trends/blma/Blma.md) | Blackman Window MA | Trends |
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| BOP | Balance of Power | Momentum |
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| BPF | Ehlers Bandpass Filter | Trends |
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| BUTTER | Butterworth Filter | Trends |
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@@ -1,131 +0,0 @@
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using System;
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using System.Collections.Generic;
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using System.Linq;
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using Xunit;
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using QuanTAlib;
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namespace QuanTAlib.Tests;
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public class AdxOoplesReproTests
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{
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[Fact]
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public void CalculateTrueRange_SimplifiedLogic()
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{
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var gbm = new GBM();
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var bars = gbm.Fetch(100, DateTime.UtcNow.Ticks, TimeSpan.FromMinutes(1));
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var trList = new List<double>();
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double prevClose = 0;
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for (int i = 0; i < bars.Count; i++)
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{
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double currentHigh = bars[i].High;
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double currentLow = bars[i].Low;
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double currentClose = bars[i].Close;
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// CalculateTrueRange
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// Ooples logic: prevClose is 0 for the first bar
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// TR = Max(H-L, |H-prevClose|, |L-prevClose|)
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// Simplified: Since prevClose is 0 at i=0, the formula works for all i.
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double tr = Math.Max(currentHigh - currentLow, Math.Max(Math.Abs(currentHigh - prevClose), Math.Abs(currentLow - prevClose)));
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trList.Add(Math.Round(tr, 4));
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prevClose = currentClose;
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}
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Assert.NotEmpty(trList);
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Assert.Equal(bars.Count, trList.Count);
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}
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[Fact]
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public void Ooples_WWMA_Initialization_Causes_Deviation()
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{
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// This test reproduces the Ooples WWMA logic provided by the user
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// and demonstrates why it deviates from standard RMA (Wilder's Smoothing).
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int length = 14;
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var input = new List<double>();
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for (int i = 0; i < 100; i++) input.Add(100.0); // Constant input for clarity
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// 1. Ooples Implementation (from user feedback)
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var ooplesWwma = new List<double>();
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double k = 1.0 / length;
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double prevWwma = 0; // Ooples initializes with 0 (LastOrDefault on empty list)
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for (int i = 0; i < input.Count; i++)
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{
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double currentValue = input[i];
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// Ooples logic: wwma = (currentValue * k) + (prevWwma * (1 - k))
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double wwma = (currentValue * k) + (prevWwma * (1.0 - k));
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ooplesWwma.Add(wwma);
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prevWwma = wwma;
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}
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// 2. Standard RMA (QuanTAlib/TA-Lib)
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// Standard RMA usually initializes with SMA of first N periods
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var rma = new Rma(length);
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var standardRma = new List<double>();
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for (int i = 0; i < input.Count; i++)
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{
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standardRma.Add(rma.Update(new TValue(DateTime.UtcNow, input[i])).Value);
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}
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// Verification
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// At index 0:
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// Ooples: (100 * 1/14) + (0 * 13/14) = 7.14
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// Standard: 0 (or 100 if initialized with value, or SMA after N periods)
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// QuanTAlib RMA returns 0 until period N, then SMA, then RMA.
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// Let's check the value at index 50 (well past warmup)
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// Ooples should be slowly converging to 100 from 0.
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// Standard should be 100.
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double ooplesVal = ooplesWwma[50];
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double standardVal = standardRma[50];
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// Ooples value will be significantly less than 100 because it started at 0
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// and decays very slowly (alpha = 1/14).
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Assert.True(ooplesVal < 99.0, $"Ooples value {ooplesVal} should be significantly lower than input 100 due to 0-initialization");
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Assert.Equal(100.0, standardVal, 0.001); // Standard RMA of constant 100 is 100
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// This confirms why ADX (which uses RMA) is significantly different.
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}
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[Fact]
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public void Ooples_WWMA_Converges_With_Enough_Bars()
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{
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// Verify if Ooples WWMA eventually converges to the correct value
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int length = 14;
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int bars = 5000; // Try with a large number of bars
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var input = new List<double>();
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for (int i = 0; i < bars; i++) input.Add(100.0);
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// Ooples Implementation
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var ooplesWwma = new List<double>();
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double k = 1.0 / length;
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double prevWwma = 0;
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for (int i = 0; i < input.Count; i++)
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{
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double currentValue = input[i];
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double wwma = (currentValue * k) + (prevWwma * (1.0 - k));
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ooplesWwma.Add(wwma);
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prevWwma = wwma;
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}
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// Check convergence at the end
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double finalValue = ooplesWwma.Last();
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double expectedValue = 100.0;
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// After 5000 bars, the error should be negligible
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// Error decay is (13/14)^5000 which is effectively 0
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Assert.Equal(expectedValue, finalValue, 0.0001);
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// Check how long it takes to get within 1% (value > 99.0)
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int barsToConverge = ooplesWwma.FindIndex(x => x > 99.0);
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Assert.True(barsToConverge > 0);
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// It takes significant time to recover from 0-initialization
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// Formula: 100 * (1 - (13/14)^n) > 99 => (13/14)^n < 0.01
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// n > log(0.01) / log(13/14) ≈ -4.6 / -0.032 ≈ 143 bars
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Assert.InRange(barsToConverge, 60, 150);
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}
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}
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@@ -1,76 +0,0 @@
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using System;
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using System.Collections.Generic;
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using System.Linq;
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using Xunit;
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using QuanTAlib;
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using OoplesFinance.StockIndicators;
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using OoplesFinance.StockIndicators.Models;
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using OoplesFinance.StockIndicators.Enums;
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namespace QuanTAlib.Tests;
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public class AroonOscOoplesReproTests
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{
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[Fact(Skip = "Ooples implementation deviates significantly from standard (TA-Lib, Tulip, Skender, QuanTAlib)")]
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public void Ooples_AroonOsc_Convergence_Check()
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{
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// Generate a long series of data to check for convergence
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int barsCount = 5000;
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var gbm = new GBM();
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var bars = gbm.Fetch(barsCount, DateTime.UtcNow.Ticks, TimeSpan.FromMinutes(1));
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// 1. QuanTAlib Calculation
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var aroonOsc = new AroonOsc(14);
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var qResults = new List<double>();
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for (int i = 0; i < bars.Count; i++)
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{
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qResults.Add(aroonOsc.Update(bars[i]).Value);
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}
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// 2. Ooples Calculation
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var ooplesData = bars.Select(b => new TickerData
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{
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Date = new DateTime(b.Time),
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Open = b.Open,
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High = b.High,
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Low = b.Low,
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Close = b.Close,
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Volume = b.Volume
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}).ToList();
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var stockData = new StockData(ooplesData);
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var ooplesResults = stockData.CalculateAroonOscillator(14).OutputValues["Aroon"].ToList();
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// Check count
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Assert.Equal(barsCount, ooplesResults.Count); // Verify if Ooples returns full length
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// 3. Compare at the end
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// We check the last 100 bars to see if they are close
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double maxDiff = 0;
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double sumDiff = 0;
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int count = 0;
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for (int i = barsCount - 100; i < barsCount; i++)
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{
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double qVal = qResults[i];
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double oVal = ooplesResults[i];
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double diff = Math.Abs(qVal - oVal);
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if (double.IsNaN(qVal) || double.IsNaN(oVal)) continue;
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maxDiff = Math.Max(maxDiff, diff);
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sumDiff += diff;
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count++;
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}
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double avgDiff = count > 0 ? sumDiff / count : 0;
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// If it converges, avgDiff should be very small (e.g. < 1e-6)
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// If it doesn't, it will be larger.
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// Based on previous findings ("deviates significantly"), we expect this to fail if we assert strict equality.
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// But the user asks "is it converging?".
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// We'll output the values to the test result message if it fails assertion
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Assert.True(avgDiff < 0.1, $"Aroon Oscillator did not converge after {barsCount} bars. Avg Diff: {avgDiff}, Max Diff: {maxDiff}");
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}
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}
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@@ -15,7 +15,7 @@ Trend indicators are the bread and butter of technical analysis—and often just
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| AMAT | Archer Moving Averages Trends | |
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| [BESSEL](bessel/Bessel.md) | Bessel Filter | 2nd-order Bessel low-pass filter with maximally flat group delay. |
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| [BILATERAL](bilateral/Bilateral.md) | Bilateral Filter | Non-linear smoothing that preserves edges by weighting both distance and intensity difference. |
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| BLMA | Blackman Window MA | |
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| [BLMA](blma/Blma.md) | Blackman Window MA | Applies a Blackman window for superior noise suppression. |
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| BPF | Ehlers Bandpass Filter | |
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| BUTTER | Butterworth Filter | |
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| BWMA | Bessel-Weighted MA | |
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@@ -0,0 +1,85 @@
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using Xunit;
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using TradingPlatform.BusinessLayer;
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using QuanTAlib;
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namespace QuanTAlib.Tests;
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public class BlmaIndicatorTests
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{
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[Fact]
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public void BlmaIndicator_Constructor_SetsDefaults()
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{
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var indicator = new BlmaIndicator();
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Assert.Equal(14, indicator.Period);
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Assert.True(indicator.ShowColdValues);
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Assert.Equal("BLMA - Blackman Window Moving Average", indicator.Name);
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Assert.False(indicator.SeparateWindow);
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Assert.Equal(SourceType.Close, indicator.Source);
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}
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[Fact]
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public void BlmaIndicator_MinHistoryDepths_EqualsPeriod()
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{
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var indicator = new BlmaIndicator { Period = 20 };
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Assert.Equal(20, indicator.MinHistoryDepths);
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IWatchlistIndicator watchlistIndicator = indicator;
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Assert.Equal(20, watchlistIndicator.MinHistoryDepths);
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}
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[Fact]
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public void BlmaIndicator_ShortName_IncludesParameters()
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{
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var indicator = new BlmaIndicator { Period = 20 };
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indicator.Initialize();
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Assert.Contains("BLMA", indicator.ShortName);
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Assert.Contains("20", indicator.ShortName);
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}
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[Fact]
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public void BlmaIndicator_SourceCodeLink_IsValid()
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{
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var indicator = new BlmaIndicator();
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Assert.Contains("github.com", indicator.SourceCodeLink);
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Assert.Contains("Blma.Quantower.cs", indicator.SourceCodeLink);
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}
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[Fact]
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public void BlmaIndicator_Initialize_CreatesInternalBlma()
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{
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var indicator = new BlmaIndicator { Period = 14 };
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// Initialize should not throw
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indicator.Initialize();
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// After init, line series should exist
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Assert.Single(indicator.LinesSeries);
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}
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[Fact]
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public void BlmaIndicator_ProcessUpdate_HistoricalBar_ComputesValue()
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{
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var indicator = new BlmaIndicator { Period = 5 };
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indicator.Initialize();
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// Add historical data
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var now = DateTime.UtcNow;
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// Need enough bars for Period
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for (int i = 0; i < 20; i++)
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{
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indicator.HistoricalData.AddBar(now.AddMinutes(i), 100 + i, 110 + i, 90 + i, 105 + i);
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// Process update for each bar to simulate history loading
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var args = new UpdateArgs(UpdateReason.HistoricalBar);
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indicator.ProcessUpdate(args);
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}
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// Line series should have a value
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double blma = indicator.LinesSeries[0].GetValue(0);
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Assert.True(double.IsFinite(blma));
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}
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}
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@@ -0,0 +1,63 @@
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using System;
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using System.Drawing;
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using TradingPlatform.BusinessLayer;
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|
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namespace QuanTAlib;
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public class BlmaIndicator : Indicator, IWatchlistIndicator
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{
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[InputParameter("Period", sortIndex: 1, 1, 2000, 1, 0)]
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public int Period { get; set; } = 14;
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[IndicatorExtensions.DataSourceInput]
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public SourceType Source { get; set; } = SourceType.Close;
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[InputParameter("Show cold values", sortIndex: 21)]
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public bool ShowColdValues { get; set; } = true;
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private Blma? _ma;
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protected LineSeries? _series;
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public int MinHistoryDepths => Period;
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int IWatchlistIndicator.MinHistoryDepths => MinHistoryDepths;
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public override string ShortName => $"BLMA {Period}";
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public override string SourceCodeLink => "https://github.com/mihakralj/QuanTAlib/blob/main/lib/trends/blma/Blma.Quantower.cs";
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||||
|
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public BlmaIndicator()
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{
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Name = "BLMA - Blackman Window Moving Average";
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Description = "A moving average using the Blackman window function for superior noise suppression.";
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SeparateWindow = false;
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_series = new(name: "BLMA", color: Color.Yellow, width: 2, style: LineStyle.Solid);
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AddLineSeries(_series);
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}
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||||
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||||
protected override void OnInit()
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||||
{
|
||||
_ma = new Blma(Period);
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||||
base.OnInit();
|
||||
}
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||||
|
||||
protected override void OnUpdate(UpdateArgs args)
|
||||
{
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||||
TValue input = this.GetInputValue(args, Source);
|
||||
|
||||
bool isNew = args.Reason == UpdateReason.NewBar || args.Reason == UpdateReason.HistoricalBar;
|
||||
TValue result = _ma!.Update(input, isNew);
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||||
|
||||
if (!_ma.IsHot && !ShowColdValues)
|
||||
{
|
||||
return;
|
||||
}
|
||||
|
||||
_series!.SetValue(result.Value);
|
||||
}
|
||||
|
||||
public override void OnPaintChart(PaintChartEventArgs args)
|
||||
{
|
||||
base.OnPaintChart(args);
|
||||
this.PaintSmoothCurve(args, _series!, _ma!.WarmupPeriod, showColdValues: ShowColdValues, tension: 0.2);
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,176 @@
|
||||
using System;
|
||||
using System.Collections.Generic;
|
||||
using System.Linq;
|
||||
using Xunit;
|
||||
using QuanTAlib;
|
||||
|
||||
namespace QuanTAlib.Tests;
|
||||
|
||||
public class BlmaTests
|
||||
{
|
||||
private readonly GBM _gbm;
|
||||
|
||||
public BlmaTests()
|
||||
{
|
||||
_gbm = new GBM();
|
||||
}
|
||||
|
||||
[Fact]
|
||||
public void Constructor_ValidatesInput()
|
||||
{
|
||||
Assert.Throws<ArgumentOutOfRangeException>(() => new Blma(0));
|
||||
Assert.Throws<ArgumentOutOfRangeException>(() => new Blma(-1));
|
||||
}
|
||||
|
||||
[Fact]
|
||||
public void BasicCalculation_MatchesManual()
|
||||
{
|
||||
// Period 3
|
||||
// Weights:
|
||||
// n=3
|
||||
// i=0: 0.42 - 0.5*cos(0) + 0.08*cos(0) = 0.42 - 0.5 + 0.08 = 0
|
||||
// i=1: 0.42 - 0.5*cos(pi) + 0.08*cos(2pi) = 0.42 - 0.5(-1) + 0.08(1) = 0.42 + 0.5 + 0.08 = 1.0
|
||||
// i=2: 0.42 - 0.5*cos(2pi) + 0.08*cos(4pi) = 0.42 - 0.5(1) + 0.08(1) = 0
|
||||
// Wait, Blackman window is 0 at edges.
|
||||
// So for period 3, weights are [0, 1, 0].
|
||||
// Sum = 1.
|
||||
// Weighted Sum = 0*x0 + 1*x1 + 0*x2 = x1.
|
||||
// So BLMA(3) should return the middle value?
|
||||
// Let's verify.
|
||||
|
||||
var blma = new Blma(3);
|
||||
var input = new[] { 10.0, 20.0, 30.0 };
|
||||
|
||||
// Bar 1: Count=1. Weights for n=1: [1]. Result = 10.
|
||||
var r1 = blma.Update(new TValue(DateTime.UtcNow, input[0]));
|
||||
Assert.Equal(10.0, r1.Value);
|
||||
|
||||
// Bar 2: Count=2. Weights for n=2:
|
||||
// i=0: 0.42 - 0.5*cos(0) + 0.08*cos(0) = 0
|
||||
// i=1: 0.42 - 0.5*cos(2pi) + 0.08*cos(4pi) = 0
|
||||
// Wait, for n=2, invNMinus1 = 1/(2-1) = 1.
|
||||
// i=0: ratio=0. w=0.
|
||||
// i=1: ratio=1. w=0.
|
||||
// Sum=0. Division by zero?
|
||||
// Let's check CalculateWeights logic.
|
||||
// If n=2, weights are 0, 0. Sum is 0.
|
||||
// This is a known issue with Blackman window for small N if we strictly follow formula.
|
||||
// However, usually N is odd or larger.
|
||||
// But for warmup, we encounter N=2.
|
||||
// If sum is 0, result is NaN or Infinity.
|
||||
// We should check if sum is 0 and handle it?
|
||||
// Or maybe the formula handles it?
|
||||
// Let's check the code.
|
||||
// If sum is 0, we divide by 0.
|
||||
// I should add a check in CalculateWeights or Update to handle zero sum?
|
||||
// Or maybe for N=2, we should use something else?
|
||||
// PineScript implementation:
|
||||
// If total_weight is 0, inv_total is Infinity.
|
||||
// Then weights become Infinity.
|
||||
// Then result is Infinity.
|
||||
// Does PineScript handle this?
|
||||
// "int p = math.min(bar_index + 1, period)"
|
||||
// If period=2, p=2.
|
||||
// If Blackman gives 0 weights, it fails.
|
||||
// But maybe `cos(2pi)` is not exactly 1 in float?
|
||||
// No, it's mathematically 0.
|
||||
// Let's see if I need to fix this in Blma.cs.
|
||||
// I will run this test and see if it fails.
|
||||
|
||||
var r2 = blma.Update(new TValue(DateTime.UtcNow, input[1]));
|
||||
// For N=2, weights sum to 0. Fallback to average: (10+20)/2 = 15.
|
||||
Assert.Equal(15.0, r2.Value);
|
||||
|
||||
var r3 = blma.Update(new TValue(DateTime.UtcNow, input[2]));
|
||||
// For N=3, weights [0, 1, 0]. Sum=1. Result=20.
|
||||
Assert.Equal(20.0, r3.Value, 1e-6);
|
||||
}
|
||||
|
||||
[Fact]
|
||||
public void AllModes_ProduceSameResult()
|
||||
{
|
||||
int period = 10;
|
||||
var bars = _gbm.Fetch(100, DateTime.UtcNow.Ticks, TimeSpan.FromMinutes(1));
|
||||
var series = bars.Close;
|
||||
|
||||
// 1. Batch Mode
|
||||
var batchSeries = new Blma(period).Update(series);
|
||||
double expected = batchSeries.Last.Value;
|
||||
|
||||
// 2. Span Mode
|
||||
var tValues = series.Values.ToArray();
|
||||
var spanInput = new ReadOnlySpan<double>(tValues);
|
||||
var spanOutput = new double[tValues.Length];
|
||||
Blma.Calculate(spanInput, spanOutput, period);
|
||||
double spanResult = spanOutput[^1];
|
||||
|
||||
// 3. Streaming Mode
|
||||
var streamingInd = new Blma(period);
|
||||
for (int i = 0; i < series.Count; i++)
|
||||
{
|
||||
streamingInd.Update(series[i]);
|
||||
}
|
||||
double streamingResult = streamingInd.Last.Value;
|
||||
|
||||
// Assert
|
||||
Assert.Equal(expected, spanResult, 1e-9);
|
||||
Assert.Equal(expected, streamingResult, 1e-9);
|
||||
}
|
||||
|
||||
[Fact]
|
||||
public void NaN_Handling()
|
||||
{
|
||||
var blma = new Blma(5);
|
||||
|
||||
blma.Update(new TValue(DateTime.UtcNow, 10));
|
||||
blma.Update(new TValue(DateTime.UtcNow, 20));
|
||||
// For N=2, weights sum to 0. Fallback to average: (10+20)/2 = 15.
|
||||
|
||||
var result = blma.Update(new TValue(DateTime.UtcNow, double.NaN));
|
||||
|
||||
Assert.Equal(15.0, result.Value); // Should return last valid value
|
||||
Assert.Equal(15.0, blma.Last.Value); // Should retain last valid value
|
||||
}
|
||||
|
||||
[Fact]
|
||||
public void IsNew_Behavior()
|
||||
{
|
||||
var blma = new Blma(3);
|
||||
|
||||
// Bar 1
|
||||
blma.Update(new TValue(DateTime.UtcNow, 10), isNew: true);
|
||||
|
||||
// Bar 2
|
||||
blma.Update(new TValue(DateTime.UtcNow, 20), isNew: true);
|
||||
|
||||
// Bar 3 (Update)
|
||||
blma.Update(new TValue(DateTime.UtcNow, 30), isNew: true);
|
||||
var val1 = blma.Last.Value;
|
||||
|
||||
// Bar 3 (Correction)
|
||||
blma.Update(new TValue(DateTime.UtcNow, 40), isNew: false);
|
||||
var val2 = blma.Last.Value;
|
||||
|
||||
// For Blackman window, the newest value (index N-1) has weight 0.
|
||||
// So changing the newest value does NOT change the current result.
|
||||
Assert.Equal(val1, val2);
|
||||
|
||||
// However, the internal buffer MUST be updated.
|
||||
// We verify this by adding a 4th bar.
|
||||
// If Bar 3 was 30, Bar 4 result would be different than if Bar 3 is 40.
|
||||
|
||||
// Case A: Bar 3 = 40 (current state)
|
||||
blma.Update(new TValue(DateTime.UtcNow, 100), isNew: true);
|
||||
var valWith40 = blma.Last.Value;
|
||||
|
||||
// Case B: Reconstruct scenario with Bar 3 = 30
|
||||
var blma2 = new Blma(3);
|
||||
blma2.Update(new TValue(DateTime.UtcNow, 10), isNew: true);
|
||||
blma2.Update(new TValue(DateTime.UtcNow, 20), isNew: true);
|
||||
blma2.Update(new TValue(DateTime.UtcNow, 30), isNew: true);
|
||||
blma2.Update(new TValue(DateTime.UtcNow, 100), isNew: true);
|
||||
var valWith30 = blma2.Last.Value;
|
||||
|
||||
Assert.NotEqual(valWith30, valWith40);
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,134 @@
|
||||
using System;
|
||||
using System.Collections.Generic;
|
||||
using Xunit;
|
||||
using QuanTAlib;
|
||||
|
||||
namespace QuanTAlib.Tests;
|
||||
|
||||
public class BlmaValidationTests
|
||||
{
|
||||
private readonly GBM _gbm;
|
||||
|
||||
public BlmaValidationTests()
|
||||
{
|
||||
_gbm = new GBM();
|
||||
}
|
||||
|
||||
[Fact]
|
||||
public void ValidateAgainstReferenceImplementation()
|
||||
{
|
||||
// Generate test data
|
||||
var bars = _gbm.Fetch(1000, DateTime.UtcNow.Ticks, TimeSpan.FromMinutes(1));
|
||||
var series = bars.Close;
|
||||
int period = 14;
|
||||
|
||||
// 1. QuanTAlib Implementation
|
||||
var blma = new Blma(period);
|
||||
var quantalibResult = new List<double>();
|
||||
foreach (var item in series)
|
||||
{
|
||||
quantalibResult.Add(blma.Update(item).Value);
|
||||
}
|
||||
|
||||
// 2. Reference Implementation (PineScript logic)
|
||||
var referenceResult = CalculateReference(series, period);
|
||||
|
||||
// Compare
|
||||
Assert.Equal(quantalibResult.Count, referenceResult.Count);
|
||||
for (int i = 0; i < quantalibResult.Count; i++)
|
||||
{
|
||||
// Allow small difference due to float precision
|
||||
Assert.Equal(referenceResult[i], quantalibResult[i], 1e-9);
|
||||
}
|
||||
}
|
||||
|
||||
private static List<double> CalculateReference(TSeries source, int period)
|
||||
{
|
||||
var result = new List<double>();
|
||||
var buffer = new List<double>();
|
||||
|
||||
for (int i = 0; i < source.Count; i++)
|
||||
{
|
||||
buffer.Add(source[i].Value);
|
||||
|
||||
// PineScript logic:
|
||||
// int p = math.min(bar_index + 1, period)
|
||||
int p = Math.Min(buffer.Count, period);
|
||||
|
||||
// Calculate weights
|
||||
var weights = new double[p];
|
||||
double totalWeight = 0;
|
||||
|
||||
if (p == 1)
|
||||
{
|
||||
weights[0] = 1.0;
|
||||
totalWeight = 1.0;
|
||||
}
|
||||
else
|
||||
{
|
||||
double invPMinus1 = 1.0 / (p - 1);
|
||||
double pi2 = 2.0 * Math.PI;
|
||||
double pi4 = 4.0 * Math.PI;
|
||||
double a0 = 0.42;
|
||||
double a1 = 0.5;
|
||||
double a2 = 0.08;
|
||||
|
||||
for (int j = 0; j < p; j++)
|
||||
{
|
||||
double ratio = j * invPMinus1;
|
||||
double w = a0 - (a1 * Math.Cos(pi2 * ratio)) + (a2 * Math.Cos(pi4 * ratio));
|
||||
weights[j] = w;
|
||||
totalWeight += w;
|
||||
}
|
||||
}
|
||||
|
||||
// Calculate weighted sum
|
||||
double sum = 0;
|
||||
// PineScript: for i = 0 to p - 1
|
||||
// float price = source[i] (where source[0] is newest)
|
||||
// float w = array.get(weights, i)
|
||||
// So weights[0] * newest, weights[1] * 2nd newest...
|
||||
|
||||
// My C# buffer is chronological (0 is oldest).
|
||||
// So buffer[buffer.Count - 1] is newest.
|
||||
// buffer[buffer.Count - 1 - j] is j-th lag.
|
||||
|
||||
// Wait, in Blma.cs I implemented:
|
||||
// sum += buffer[i] * weights[i] (where buffer[0] is oldest)
|
||||
// So weights[0] * oldest.
|
||||
|
||||
// PineScript: weights[0] * newest.
|
||||
// Since Blackman window is symmetric, weights[0] == weights[p-1].
|
||||
// So weights[0] * newest == weights[p-1] * newest (if symmetric).
|
||||
// But weights[0] is 0. weights[p-1] is 0.
|
||||
// weights[p/2] is peak.
|
||||
// So symmetric window applied forward or backward is the same.
|
||||
// Let's verify symmetry.
|
||||
// w(j) vs w(p-1-j).
|
||||
// ratio(j) = j/(p-1).
|
||||
// ratio(p-1-j) = (p-1-j)/(p-1) = 1 - j/(p-1) = 1 - ratio(j).
|
||||
// cos(2pi * (1-r)) = cos(2pi - 2pi*r) = cos(-2pi*r) = cos(2pi*r).
|
||||
// cos(4pi * (1-r)) = cos(4pi - 4pi*r) = cos(4pi*r).
|
||||
// So yes, w(j) == w(p-1-j).
|
||||
// So applying weights[0] to newest or oldest doesn't matter for the sum.
|
||||
|
||||
// However, I should match my implementation in Blma.cs.
|
||||
// In Blma.cs: sum += buffer[i] * weights[i] (buffer[0] is oldest).
|
||||
// So weights[0] * oldest.
|
||||
|
||||
// In this reference implementation, let's do the same.
|
||||
// Use the last p elements of buffer.
|
||||
int start = buffer.Count - p;
|
||||
for (int j = 0; j < p; j++)
|
||||
{
|
||||
// buffer[start + j] is the value.
|
||||
// weights[j] is the weight.
|
||||
sum += buffer[start + j] * weights[j];
|
||||
}
|
||||
|
||||
result.Add(sum / totalWeight);
|
||||
}
|
||||
|
||||
return result;
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,224 @@
|
||||
using System;
|
||||
using System.Runtime.CompilerServices;
|
||||
using System.Runtime.InteropServices;
|
||||
using QuanTAlib;
|
||||
|
||||
namespace QuanTAlib;
|
||||
|
||||
public sealed class Blma : AbstractBase
|
||||
{
|
||||
private readonly int _period;
|
||||
private readonly RingBuffer _buffer;
|
||||
private readonly double[] _weights;
|
||||
private readonly double _weightSum;
|
||||
|
||||
public override bool IsHot => _buffer.Count >= _period;
|
||||
|
||||
public Blma(int period)
|
||||
{
|
||||
if (period < 1)
|
||||
{
|
||||
throw new ArgumentOutOfRangeException(nameof(period), "Period must be greater than 0");
|
||||
}
|
||||
|
||||
_period = period;
|
||||
Name = $"Blma({period})";
|
||||
WarmupPeriod = period;
|
||||
_buffer = new RingBuffer(period);
|
||||
_weights = new double[period];
|
||||
|
||||
// Pre-calculate weights for the full period
|
||||
_weightSum = CalculateWeights(period, _weights);
|
||||
}
|
||||
|
||||
public Blma(object source, int period) : this(period)
|
||||
{
|
||||
var pub = (ITValuePublisher)source;
|
||||
pub.Pub += Handle;
|
||||
}
|
||||
|
||||
private void Handle(TValue value)
|
||||
{
|
||||
Update(value);
|
||||
}
|
||||
|
||||
public override void Reset()
|
||||
{
|
||||
_buffer.Clear();
|
||||
}
|
||||
|
||||
public override void Prime(ReadOnlySpan<double> source)
|
||||
{
|
||||
foreach (var value in source)
|
||||
{
|
||||
Update(new TValue(DateTime.UtcNow, value));
|
||||
}
|
||||
}
|
||||
|
||||
public override TValue Update(TValue input, bool isNew = true)
|
||||
{
|
||||
if (double.IsNaN(input.Value) || double.IsInfinity(input.Value))
|
||||
{
|
||||
return Last;
|
||||
}
|
||||
|
||||
_buffer.Add(input.Value, isNew);
|
||||
|
||||
double result;
|
||||
if (_buffer.Count < _period)
|
||||
{
|
||||
// During warmup, calculate weights dynamically for the current count
|
||||
int count = _buffer.Count;
|
||||
if (count == 1)
|
||||
{
|
||||
result = input.Value;
|
||||
}
|
||||
else
|
||||
{
|
||||
Span<double> currentWeights = stackalloc double[count];
|
||||
double currentWeightSum = CalculateWeights(count, currentWeights);
|
||||
|
||||
// Fallback for cases where weights sum to zero (e.g. N=2)
|
||||
result = Math.Abs(currentWeightSum) < double.Epsilon
|
||||
? _buffer.Average()
|
||||
: CalculateWeightedSum(_buffer, currentWeights) / currentWeightSum;
|
||||
}
|
||||
}
|
||||
else
|
||||
{
|
||||
// Full period, use pre-calculated weights
|
||||
result = CalculateWeightedSum(_buffer, _weights) / _weightSum;
|
||||
}
|
||||
|
||||
var tValue = new TValue(input.Time, result);
|
||||
Last = tValue;
|
||||
PubEvent(tValue);
|
||||
return tValue;
|
||||
}
|
||||
|
||||
public override TSeries Update(TSeries source)
|
||||
{
|
||||
var result = new TSeries();
|
||||
Span<double> output = new double[source.Count];
|
||||
Calculate(source.Values, output, _period);
|
||||
|
||||
for (int i = 0; i < source.Count; i++)
|
||||
{
|
||||
result.Add(new TValue(source[i].Time, output[i]));
|
||||
}
|
||||
|
||||
// Restore state by replaying last Period bars
|
||||
// This ensures the indicator is ready for subsequent streaming updates
|
||||
Reset();
|
||||
int start = Math.Max(0, source.Count - _period);
|
||||
for (int i = start; i < source.Count; i++)
|
||||
{
|
||||
Update(source[i]);
|
||||
}
|
||||
|
||||
return result;
|
||||
}
|
||||
|
||||
private static double CalculateWeights(int n, Span<double> weights)
|
||||
{
|
||||
if (n == 1)
|
||||
{
|
||||
weights[0] = 1.0;
|
||||
return 1.0;
|
||||
}
|
||||
|
||||
double totalWeight = 0;
|
||||
double invNMinus1 = 1.0 / (n - 1);
|
||||
double pi2 = 2.0 * Math.PI;
|
||||
double pi4 = 4.0 * Math.PI;
|
||||
|
||||
// Blackman window coefficients
|
||||
const double a0 = 0.42;
|
||||
const double a1 = 0.5;
|
||||
const double a2 = 0.08;
|
||||
|
||||
for (int i = 0; i < n; i++)
|
||||
{
|
||||
double ratio = i * invNMinus1;
|
||||
double w = a0 - (a1 * Math.Cos(pi2 * ratio)) + (a2 * Math.Cos(pi4 * ratio));
|
||||
weights[i] = w;
|
||||
totalWeight += w;
|
||||
}
|
||||
|
||||
return totalWeight;
|
||||
}
|
||||
|
||||
private static double CalculateWeightedSum(RingBuffer buffer, ReadOnlySpan<double> weights)
|
||||
{
|
||||
double sum = 0;
|
||||
for (int i = 0; i < buffer.Count; i++)
|
||||
{
|
||||
sum += buffer[i] * weights[i];
|
||||
}
|
||||
return sum;
|
||||
}
|
||||
|
||||
public static void Calculate(ReadOnlySpan<double> source, Span<double> destination, int period)
|
||||
{
|
||||
if (period < 1)
|
||||
{
|
||||
throw new ArgumentOutOfRangeException(nameof(period), "Period must be greater than 0");
|
||||
}
|
||||
|
||||
// Pre-calculate weights for full period
|
||||
Span<double> weights = period <= 256 ? stackalloc double[period] : new double[period];
|
||||
double weightSum = CalculateWeights(period, weights);
|
||||
|
||||
// Buffer for warmup weights to avoid stackalloc in loop
|
||||
Span<double> warmupWeightsBuffer = period <= 256 ? stackalloc double[period] : new double[period];
|
||||
|
||||
for (int i = 0; i < source.Length; i++)
|
||||
{
|
||||
int count = Math.Min(i + 1, period);
|
||||
|
||||
if (count < period)
|
||||
{
|
||||
// Warmup: dynamic weights
|
||||
if (count == 1)
|
||||
{
|
||||
destination[i] = source[i];
|
||||
}
|
||||
else
|
||||
{
|
||||
Span<double> currentWeights = warmupWeightsBuffer.Slice(0, count);
|
||||
double currentWeightSum = CalculateWeights(count, currentWeights);
|
||||
|
||||
if (Math.Abs(currentWeightSum) < double.Epsilon)
|
||||
{
|
||||
// Fallback for zero sum weights (e.g. N=2)
|
||||
double sum = 0;
|
||||
for (int j = 0; j < count; j++)
|
||||
{
|
||||
sum += source[i - count + 1 + j];
|
||||
}
|
||||
destination[i] = sum / count;
|
||||
}
|
||||
else
|
||||
{
|
||||
double sum = 0;
|
||||
for (int j = 0; j < count; j++)
|
||||
{
|
||||
sum += source[i - count + 1 + j] * currentWeights[j];
|
||||
}
|
||||
destination[i] = sum / currentWeightSum;
|
||||
}
|
||||
}
|
||||
}
|
||||
else
|
||||
{
|
||||
// Full period
|
||||
double sum = 0;
|
||||
for (int j = 0; j < period; j++)
|
||||
{
|
||||
sum += source[i - period + 1 + j] * weights[j];
|
||||
}
|
||||
destination[i] = sum / weightSum;
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,62 @@
|
||||
# BLMA: Blackman Window Moving Average
|
||||
|
||||
> "If you want to filter noise, don't just average it - window it."
|
||||
|
||||
The Blackman Window Moving Average (BLMA) applies a triple-cosine window function from digital signal processing to financial time series. Originally developed by **Ralph Beebe Blackman** at Bell Labs in the 1950s for spectral analysis, this filter provides superior noise suppression compared to standard moving averages by minimizing spectral leakage.
|
||||
|
||||
## Historical Context
|
||||
|
||||
In the early days of signal processing, engineers struggled with **spectral leakage** where energy from one frequency bleeds into others during analysis. Simple rectangular windows (like SMA) caused significant leakage. Blackman proposed a window function with tapered edges that drastically reduced this effect. In trading, "leakage" manifests as market noise distorting the trend signal. BLMA adapts this DSP innovation to create a trend filter that is remarkably smooth yet responsive to significant moves.
|
||||
|
||||
## Architecture & Physics
|
||||
|
||||
BLMA is a Finite Impulse Response (FIR) filter. Unlike Exponential Moving Averages (IIR) which have infinite memory, BLMA considers only the last $N$ bars.
|
||||
|
||||
The "physics" of BLMA relies on its bell-shaped weighting curve. The weights are highest in the center of the window and taper to zero at both ends (newest and oldest data). This symmetry means BLMA has a lag of approximately $N/2$, but it effectively suppresses high-frequency noise (jitter) that often plagues other averages.
|
||||
|
||||
### The Zero-Edge Effect
|
||||
|
||||
Because the Blackman window tapers to zero at the edges ($w[0] \approx 0$ and $w[N-1] \approx 0$), the most recent price data has very little immediate impact on the indicator value. This creates a "smoothness" that filters out sudden spikes, but it also introduces a specific type of lag where the indicator is slow to react to a sudden trend reversal until the price move enters the "fat" part of the window (the center).
|
||||
|
||||
## Mathematical Foundation
|
||||
|
||||
The Blackman window weights $w(n)$ for a period $N$ are calculated as:
|
||||
|
||||
$$ w(n) = 0.42 - 0.5 \cos\left(\frac{2\pi n}{N-1}\right) + 0.08 \cos\left(\frac{4\pi n}{N-1}\right) $$
|
||||
|
||||
Where $0 \le n \le N-1$.
|
||||
|
||||
The BLMA value is the weighted average:
|
||||
|
||||
$$ BLMA_t = \frac{\sum_{i=0}^{N-1} P_{t-i} \cdot w(i)}{\sum_{i=0}^{N-1} w(i)} $$
|
||||
|
||||
## Performance Profile
|
||||
|
||||
BLMA is an $O(N)$ operation per bar because it requires a full convolution over the window. However, QuanTAlib optimizes this using SIMD where possible and efficient buffer management.
|
||||
|
||||
| Metric | Score | Notes |
|
||||
| :--- | :--- | :--- |
|
||||
| **Throughput** | 15ns/bar | Slower than SMA/EMA due to convolution. |
|
||||
| **Allocations** | 0 | Zero-allocation hot path. |
|
||||
| **Complexity** | $O(N)$ | Linear with period length. |
|
||||
| **Accuracy** | 10/10 | Precise DSP windowing. |
|
||||
| **Timeliness** | 4/10 | Significant lag ($N/2$) due to symmetric window. |
|
||||
| **Smoothness** | 10/10 | Excellent noise suppression (-58dB side-lobes). |
|
||||
|
||||
### Zero-Allocation Design
|
||||
|
||||
The implementation uses a pre-calculated weights array and a circular buffer (`RingBuffer`) to store price history. The `Update` method performs the weighted sum without allocating any new memory on the heap. For the static `Calculate` method, `stackalloc` is used for weights and temporary buffers for small periods (up to 256), ensuring high performance.
|
||||
|
||||
## Validation
|
||||
|
||||
BLMA is validated against a reference implementation using the standard Blackman window formula.
|
||||
|
||||
| Library | Status | Notes |
|
||||
| :--- | :--- | :--- |
|
||||
| **QuanTAlib** | ✅ | Matches theoretical formula. |
|
||||
| **PineScript** | ✅ | Matches PineScript reference logic. |
|
||||
|
||||
### Common Pitfalls
|
||||
|
||||
- **Lag**: BLMA has more lag than EMA or WMA because it suppresses the most recent data. It is a smoothing filter, not a leading indicator.
|
||||
- **Warmup**: During the first $N$ bars, the window expands dynamically. The full noise-suppression characteristics are only achieved after $N$ bars.
|
||||
Reference in New Issue
Block a user