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Covar, Kendall, Spearman

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Miha
2024-11-08 21:20:06 -08:00
parent fce3a783eb
commit f46a5330bf
12 changed files with 788 additions and 191 deletions
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Tests/test_eventing.cs
+3
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@@ -68,6 +68,9 @@ public class EventingTests
("Zscore", new object[] { DefaultPeriod }, new object[] { new TSeries(), DefaultPeriod }),
("Beta", new object[] { DefaultPeriod }, new object[] { new TSeries(), DefaultPeriod }),
("Corr", new object[] { DefaultPeriod }, new object[] { new TSeries(), DefaultPeriod }),
("Covar", new object[] { DefaultPeriod }, new object[] { new TSeries(), DefaultPeriod }),
("Kendall", new object[] { DefaultPeriod }, new object[] { new TSeries(), DefaultPeriod }),
("Spearman", new object[] { DefaultPeriod }, new object[] { new TSeries(), DefaultPeriod }),
("Hv", new object[] { DefaultPeriod, false }, new object[] { new TSeries(), DefaultPeriod, false }),
("Jvolty", new object[] { DefaultPeriod, 0 }, new object[] { new TSeries(), DefaultPeriod, 0 }),
("Rv", new object[] { DefaultPeriod, false }, new object[] { new TSeries(), DefaultPeriod, false }),
Tests/test_updates_statistics.cs
+21
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@@ -18,6 +18,13 @@ public class StatisticsUpdateTests : UpdateTestBase
TestDualTValueUpdate(indicator, indicator.Calc);
}
[Fact]
public void Covar_Update()
{
var indicator = new Covar(period: 14);
TestDualTValueUpdate(indicator, indicator.Calc);
}
[Fact]
public void Curvature_Update()
{
@@ -39,6 +46,13 @@ public class StatisticsUpdateTests : UpdateTestBase
TestTBarUpdate(indicator, indicator.Calc);
}
[Fact]
public void Kendall_Update()
{
var indicator = new Kendall(period: 14);
TestDualTValueUpdate(indicator, indicator.Calc);
}
[Fact]
public void Kurtosis_Update()
{
@@ -95,6 +109,13 @@ public class StatisticsUpdateTests : UpdateTestBase
TestTValueUpdate(indicator, indicator.Calc);
}
[Fact]
public void Spearman_Update()
{
var indicator = new Spearman(period: 14);
TestDualTValueUpdate(indicator, indicator.Calc);
}
[Fact]
public void Stddev_Update()
{
lib/_list.md
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@@ -0,0 +1,173 @@
# QuanTAlib Indicators Status
## Implementation Status
| Category | Done | Todo | Total |
|------------|------|------|-------|
| Averages | 33 | 0 | 33 |
| Momentum | 17 | 0 | 17 |
| Oscillators| 24 | 5 | 29 |
| Patterns | 0 | 8 | 8 |
| Statistics | 21 | 2 | 23 |
| Volatility | 31 | 4 | 35 |
| Total | 126 | 19 | 145 |
## Indicators by Category
### Averages (33/33)
✔️ AFIRMA - Adaptive FIR Moving Average
✔️ ALMA - Arnaud Legoux Moving Average
✔️ CONVOLUTION - 1D Convolution with sliding kernel
✔️ DEMA - Double Exponential Moving Average
✔️ DSMA - Dynamic Simple Moving Average
✔️ DWMA - Dynamic Weighted Moving Average
✔️ EMA - Exponential Moving Average
✔️ EPMA - Endpoint Moving Average
✔️ FRAMA - Fractal Adaptive Moving Average
✔️ FWMA - Forward Weighted Moving Average
✔️ GMA - Gaussian Moving Average
✔️ HMA - Hull Moving Average
✔️ HTIT - Hilbert Transform Instantaneous Trendline
✔️ HWMA - Hann Weighted Moving Average
✔️ JMA - Jurik Moving Average
✔️ KAMA - Kaufman Adaptive Moving Average
✔️ LTMA - Linear Time Moving Average
✔️ MAAF - Moving Average Adaptive Filter
✔️ MAMA - MESA Adaptive Moving Average (MAMA, FAMA)
✔️ MGDI - McGinley Dynamic Indicator
✔️ MMA - Modified Moving Average
✔️ PWMA - Parabolic Weighted Moving Average
✔️ QEMA - Quick Exponential Moving Average
✔️ REMA - Regularized Exponential Moving Average
✔️ RMA - Running Moving Average
✔️ SINEMA - Sine-weighted Moving Average
✔️ SMA - Simple Moving Average
✔️ SMMA - Smoothed Moving Average
✔️ T3 - Triple Exponential Moving Average (T3)
✔️ TEMA - Triple Exponential Moving Average
✔️ TRIMA - Triangular Moving Average
✔️ VIDYA - Variable Index Dynamic Average
✔️ WMA - Weighted Moving Average
✔️ ZLEMA - Zero-Lag Exponential Moving Average
### Momentum (17/17)
✔️ ADX - Average Directional Movement Index
✔️ ADXR - Average Directional Movement Index Rating
✔️ APO - Absolute Price Oscillator
✔️ DMI - Directional Movement Index (DI+, DI-)
✔️ DMX - Jurik Directional Movement Index
✔️ DPO - Detrended Price Oscillator
✔️ MACD - Moving Average Convergence/Divergence (MACD, Signal, Histogram)
✔️ MOM - Momentum
✔️ PMO - Price Momentum Oscillator
✔️ PO - Price Oscillator
✔️ PPO - Percentage Price Oscillator
✔️ PRS - Price Relative Strength
✔️ ROC - Rate of Change
✔️ TSI - True Strength Index
✔️ TRIX - 1-day ROC of TEMA
✔️ VEL - Jurik Signal Velocity
✔️ VORTEX - Vortex Indicator (VI+, VI-)
### Oscillators (24/29)
✔️ AC - Acceleration Oscillator
✔️ AO - Awesome Oscillator
✔️ AROON - Aroon oscillator (Up, Down)
✔️ BOP - Balance of Power
✔️ CCI - Commodity Channel Index
✔️ CFO - Chande Forcast Oscillator
✔️ CHOP - Choppiness Index
✔️ CMO - Chande Momentum Oscillator
✔️ COG - Ehler's Center of Gravity
✔️ COPPOCK - Coppock Curve
✔️ CRSI - Connor RSI
✔️ CTI - Ehler's Correlation Trend Indicator
✔️ DOSC - Derivative Oscillator
✔️ FISHER - Fisher Transform
✔️ EFI - Elder Ray's Force Index
✔️ RSI - Relative Strength Index
✔️ RSX - Jurik Trend Strength Index
✔️ SMI - Stochastic Momentum Index
✔️ SRSI - Stochastic RSI (SRSI, Signal)
✔️ STC - Schaff Trend Cycle
✔️ STOCH - Stochastic Oscillator (%K, %D)
✔️ TSI - True Strength Index
✔️ UO - Ultimate Oscillator
✔️ WILLR - Larry Williams' %R
FOSC - Forecast Oscillator
GATOR - Williams Alliator Oscillator (Upper Jaw, Lower Jaw, Teeth)
KDJ - KDJ Indicator (K, D, J lines)
KRI - Kairi Relative Index
RVGI - Relative Vigor Index (RVGI, Signal)
### Patterns (0/8)
DOJI - Doji Candlestick Pattern
ER - Elder Ray Pattern (Bull Power, Bear Power)
MARU - Marubozu Candlestick Pattern
PIV - Pivot Points (Support 1-3, Pivot, Resistance 1-3)
PP - Price Pivots (Support 1-3, Pivot, Resistance 1-3)
RPP - Rolling Pivot Points (Support 1-3, Pivot, Resistance 1-3)
WF - Williams Fractal
ZZ - Zig Zag Pattern
### Statistics (21/23)
✔️ BETA - Beta coefficient measuring volatility relative to market
✔️ CORR - Correlation coefficient between two series
✔️ COVAR - Covariance between two series
✔️ CURVATURE - Curvature of a time series
✔️ ENTROPY - Information entropy of a series
✔️ HURST - Hurst exponent for trend strength
✔️ KENDALL - Kendall rank correlation
✔️ KURTOSIS - Kurtosis measuring tail extremity
✔️ MAX - Maximum value over period
✔️ MEDIAN - Median value over period
✔️ MIN - Minimum value over period
✔️ MODE - Mode (most frequent value)
✔️ PERCENTILE - Percentile rank calculation
✔️ SKEW - Skewness measuring distribution asymmetry
✔️ SLOPE - Linear regression slope
✔️ SPEARMAN - Spearman rank correlation
✔️ STDDEV - Standard deviation
✔️ THEIL - Theil's U statistics for forecast accuracy
✔️ TSF - Time series forecast
✔️ VARIANCE - Statistical variance
✔️ ZSCORE - Z-score standardization
COINTEGRATION - Test for cointegrated series
GRANGER - Granger causality test
### Volatility (31/35)
✔️ ADR - Average Daily Range
✔️ AP - Andrew's Pitchfork
✔️ ATR - Average True Range
✔️ ATRP - Average True Range Percent
✔️ ATRS - ATR Trailing Stop
✔️ BBAND - Bollinger Bands® (Upper, Middle, Lower)
✔️ CCV - Close-to-Close Volatility
✔️ CE - Chandelier Exit
✔️ CV - Conditional Volatility (ARCH/GARCH)
✔️ CVI - Chaikin's Volatility
✔️ DCHN - Donchian Channels (Upper, Middle, Lower)
✔️ EWMA - Exponential Weighted Moving Average Volatility
✔️ FCB - Fractal Chaos Bands
✔️ GKV - Garman-Klass Volatility
✔️ HLV - High-Low Volatility
✔️ HV - Historical Volatility
✔️ JVOLTY - Jurik Volatility (Jvolty, Upper band, Lower band)
✔️ NATR - Normalized Average True Range
✔️ PCH - Price Channel Indicator
✔️ PV - Parkinson Volatility
✔️ RSV - Rogers-Satchell Volatility
✔️ RV - Realized Volatility
✔️ RVI - Relative Volatility Index
✔️ SV - Stochastic Volatility
✔️ TR - True Range
✔️ UI - Ulcer Index
✔️ VC - Volatility Cone (Mean, Upper Bound, Lower Bound)
✔️ VOV - Volatility of Volatility
✔️ VR - Volatility Ratio
✔️ VS - Volatility Stop (Long Stop, Short Stop)
✔️ YZV - Yang-Zhang Volatility
ICH - Ichimoku Cloud (Conversion, Base, Leading Span A, Leading Span B, Lagging Span)
KC - Keltner Channels (Upper, Middle, Lower)
PSAR - Parabolic Stop and Reverse (Value, Trend)
STARC - Starc Bands (Upper, Middle, Lower)
lib/_todolist.md
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# Stock Indicators List
## Common Indicators (Both Libraries)
| Indicator Name | Skender Method | QuanTAlib Class |
|---------------|----------------|-----------------|
| ADL - Accumulation/Distribution Line | GetAdl | Adl |
| ADOSC - Accumulation/Distribution Oscillator | GetAdo | Adosc |
| ALMA - Arnaud Legoux Moving Average | GetAlma | Alma |
| AROON - Aroon Oscillator | GetAroon | Aroon |
| ADX - Average Directional Index | GetAdx | Adx |
| ATR - Average True Range | GetAtr | Atr |
| AO - Awesome Oscillator | GetAwesome | Ao |
| CMF - Chaikin Money Flow | GetCmf | Cmf |
| CMO - Chande Momentum Oscillator | GetCmo | Cmo |
| DEMA - Double Exponential Moving Average | GetDema | Dema |
| EOM - Ease of Movement | GetEom | Eom |
| EPMA - Endpoint Moving Average | GetEpma | Epma |
| EMA - Exponential Moving Average | GetEma | Ema |
| HTIT - Hilbert Transform Instantaneous Trendline | GetHtTrendline | Htit |
| HMA - Hull Moving Average | GetHma | Hma |
| KVO - Klinger Volume Oscillator | GetKvo | Kvo |
| OBV - On-Balance Volume | GetObv | Aobv |
| PMO - Price Momentum Oscillator | GetPmo | Pmo |
| PRS - Price Relative Strength | GetPrs | Prs |
| ROC - Rate of Change | GetRoc | Roc |
| RSI - Relative Strength Index | GetRsi | Rsi |
| SMA - Simple Moving Average | GetSma | Sma |
| SMMA - Smoothed Moving Average | GetSmma | Smma |
| SLOPE - Slope and Linear Regression | GetSlope | Slope |
| STDEV - Standard Deviation | GetStdDev | Stddev |
| TRIX - Triple EMA Oscillator | GetTrix | Trix |
| TEMA - Triple Exponential Moving Average | GetTema | Tema |
| WMA - Weighted Moving Average | GetWma | Wma |
## Skender-Only Indicators
| Indicator Name | Skender Method |
|---------------|----------------|
| ATRS - ATR Trailing Stop | GetAtrStop |
| BOP - Balance of Power | GetBop |
| BETA - Beta Coefficient | GetBeta |
| BB - Bollinger Bands | GetBollingerBands |
| CE - Chandelier Exit | GetChandelier |
| CHOP - Choppiness Index | GetChop |
| CCI - Commodity Channel Index | GetCci |
| CRSI - Connors RSI | GetConnorsRsi |
| CORR - Correlation Coefficient | GetCorrelation |
| DPO - Detrended Price Oscillator | GetDpo |
| DOJI - Doji Pattern | GetDoji |
| DC - Donchian Channel | GetDonchian |
| ER - Elder-Ray | GetElderRay |
| FISH - Fisher Transform | GetFisherTransform |
| FI - Force Index | GetForceIndex |
| FCB - Fractal Chaos Bands | GetFcb |
| GATOR - Gator Oscillator | GetGator |
| HA - Heikin-Ashi | GetHeikinAshi |
| HURST - Hurst Exponent | GetHurst |
| ICH - Ichimoku Cloud | GetIchimoku |
| KC - Keltner Channels | GetKeltner |
| MARU - Marubozu Pattern | GetMarubozu |
| MFI - Money Flow Index | GetMfi |
| MAE - Moving Average Envelopes | GetMaEnvelopes |
| PSAR - Parabolic SAR | GetParabolicSar |
| PP - Pivot Points | GetPivotPoints |
| PIV - Pivots | GetPivots |
| PVO - Price Volume Oscillator | GetPvo |
| RENKO-ATR - Renko Chart ATR | GetRenkoAtr |
| RENKO - Renko Chart Standard | GetRenko |
| RPP - Rolling Pivot Points | GetRollingPivots |
| STC - Schaff Trend Cycle | GetStc |
| SDC - Standard Deviation Channels | GetStdDevChannels |
| STARC - Starc Bands | GetStarcBands |
| SMI - Stochastic Momentum Index | GetSmi |
| STOCH - Stochastic Oscillator | GetStoch |
| STOCH-RSI - Stochastic RSI | GetStochRsi |
| ST - Supertrend | GetSuperTrend |
| TR - True Range | GetTr |
| TSI - True Strength Index | GetTsi |
| UI - Ulcer Index | GetUlcerIndex |
| UO - Ultimate Oscillator | GetUltimate |
| VSS - Volatility System/Stop | GetVolatilityStop |
| VWAP - Volume Weighted Average Price | GetVwap |
| VWMA - Volume Weighted Moving Average | GetVwma |
| VTX - Vortex Indicator | GetVortex |
| WAG - Williams Alligator | GetAlligator |
| WF - Williams Fractal | GetFractal |
| ZZ - Zig Zag | GetZigZag |
## QuanTAlib-Only Indicators
| Indicator Name | QuanTAlib Class |
|---------------|-----------------|
| AC - Acceleration Oscillator | Ac |
| AFIRMA - Adaptive Firman Moving Average | Afirma |
| APO - Absolute Price Oscillator | Apo |
| ADXR - ADX Rating | Adxr |
| CONV - Convolution Moving Average | Convolution |
| CURV - Curvature | Curvature |
| DMI - Directional Movement Index | Dmi |
| DMX - Directional Movement Extended | Dmx |
| DSMA - Double Smoothed Moving Average | Dsma |
| DWMA - Dynamic Weighted Moving Average | Dwma |
| ENT - Entropy | Entropy |
| FRAMA - Fractal Adaptive Moving Average | Frama |
| FWMA - Fibonacci Weighted Moving Average | Fwma |
| GMA - Gaussian Moving Average | Gma |
| HV - Historical Volatility | Hv |
| HWMA - Hybrid Weighted Moving Average | Hwma |
| JMA - Jurik Moving Average | Jma |
| JVOL - Jurik Volatility | Jvolty |
| KURT - Kurtosis | Kurtosis |
| KAMA - Kaufman Adaptive Moving Average | Kama |
| LTMA - Laguerre Time Moving Average | Ltma |
| MAX - Maximum Value | Max |
| MAAF - Median Adaptive Antifractal | Maaf |
| MAMA - Mesa Adaptive Moving Average | Mama |
| MGDI - McGinley Dynamic Indicator | Mgdi |
| MEDIAN - Median Value | Median |
| MIN - Minimum Value | Min |
| MMA - Modified Moving Average | Mma |
| MODE - Mode Value | Mode |
| MOM - Momentum | Mom |
| PCTL - Percentile | Percentile |
| PO - Price Oscillator | Po |
| PPO - Price Percentage Oscillator | Ppo |
| PWMA - Polynomial Weighted Moving Average | Pwma |
| QEMA - Quadratic Exponential Moving Average | Qema |
| REMA - Range-Normalized Exponential Moving Average | Rema |
| RSX - Relative Strength Extended | Rsx |
| RV - Realized Volatility | Rv |
| RVI - Relative Volatility Index | Rvi |
| RMA - Rolling Moving Average | Rma |
| SINEMA - Sine-Wave Exponential Moving Average | Sinema |
| SKEW - Skewness | Skew |
| T3 - Tillson T3 Moving Average | T3 |
| TRIMA - Triangular Moving Average | Trima |
| VAR - Variance | Variance |
| VIDYA - Variable Index Dynamic Average | Vidya |
| VEL - Velocity | Vel |
| ZLEMA - Zero-Lag Exponential Moving Average | Zlema |
| ZSCORE - Z-Score | Zscore |
lib/momentum/_list.md
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@@ -6,7 +6,7 @@
✔️ DMI - Directional Movement Index (DI+, DI-)
✔️ DMX - Jurik Directional Movement Index
✔️ DPO - Detrended Price Oscillator
✔️ *MACD - Moving Average Convergence/Divergence (MACD, Signal, Histogram)
✔️ MACD - Moving Average Convergence/Divergence (MACD, Signal, Histogram)
✔️ MOM - Momentum
✔️ PMO - Price Momentum Oscillator
✔️ PO - Price Oscillator
@@ -16,4 +16,4 @@
✔️ TSI - True Strength Index
✔️ TRIX - 1-day ROC of TEMA
✔️ VEL - Jurik Signal Velocity
✔️ *VORTEX - Vortex Indicator (VI+, VI-)
✔️ VORTEX - Vortex Indicator (VI+, VI-)
lib/oscillators/_list.md
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@@ -16,13 +16,8 @@ Done: 24, Todo: 5
✔️ DOSC - Derivative Oscillator
✔️ FISHER - Fisher Transform
✔️ EFI - Elder Ray's Force Index
FOSC - Forecast Oscillator
*GATOR - Williams Alliator Oscillator (Upper Jaw, Lower Jaw, Teeth)
*KDJ - KDJ Indicator (K, D, J lines)
KRI - Kairi Relative Index
✔️ RSI - Relative Strength Index
✔️ RSX - Jurik Trend Strength Index
*RVGI - Relative Vigor Index (RVGI, Signal)
✔️ SMI - Stochastic Momentum Index
✔️ SRSI - Stochastic RSI (SRSI, Signal)
✔️ STC - Schaff Trend Cycle
@@ -30,3 +25,8 @@ KRI - Kairi Relative Index
✔️ TSI - True Strength Index
✔️ UO - Ultimate Oscillator
✔️ WILLR - Larry Williams' %R
FOSC - Forecast Oscillator
GATOR - Williams Alliator Oscillator (Upper Jaw, Lower Jaw, Teeth)
KDJ - KDJ Indicator (K, D, J lines)
KRI - Kairi Relative Index
RVGI - Relative Vigor Index (RVGI, Signal)
lib/patterns/_list.md
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@@ -2,10 +2,10 @@
Done: 0, Todo: 8
DOJI - Doji Candlestick Pattern
*ER - Elder Ray Pattern (Bull Power, Bear Power)
ER - Elder Ray Pattern (Bull Power, Bear Power)
MARU - Marubozu Candlestick Pattern
*PIV - Pivot Points (Support 1-3, Pivot, Resistance 1-3)
*PP - Price Pivots (Support 1-3, Pivot, Resistance 1-3)
*RPP - Rolling Pivot Points (Support 1-3, Pivot, Resistance 1-3)
PIV - Pivot Points (Support 1-3, Pivot, Resistance 1-3)
PP - Price Pivots (Support 1-3, Pivot, Resistance 1-3)
RPP - Rolling Pivot Points (Support 1-3, Pivot, Resistance 1-3)
WF - Williams Fractal
ZZ - Zig Zag Pattern
lib/statistics/Covar.cs
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using System.Runtime.CompilerServices;
namespace QuanTAlib;
/// <summary>
/// COVAR: Covariance
/// A statistical measure that quantifies how two variables change together. Unlike correlation,
/// covariance is not normalized and therefore is scale-dependent. A positive covariance indicates
/// that variables tend to move in the same direction, while a negative covariance indicates
/// opposite movement.
/// </summary>
/// <remarks>
/// The Covariance calculation process:
/// 1. Calculates mean of both variables
/// 2. For each pair of points, multiply their deviations from their respective means
/// 3. Sum these products and divide by the number of observations
///
/// Key characteristics:
/// - Measures linear relationship
/// - Scale-dependent measure
/// - Sign indicates direction of relationship
/// - Magnitude depends on scale of variables
/// - Basis for correlation coefficient
///
/// Formula:
/// Cov(X,Y) = Σ((x - μx)(y - μy)) / n
/// where:
/// X, Y = variables
/// μx, μy = means of X and Y
/// n = number of observations
///
/// Market Applications:
/// - Portfolio risk analysis
/// - Pairs trading strategy development
/// - Asset relationship analysis
/// - Risk factor sensitivity analysis
/// - Multi-asset portfolio optimization
///
/// Sources:
/// https://en.wikipedia.org/wiki/Covariance
/// "Modern Portfolio Theory" - Harry Markowitz
///
/// Note: Scale-dependent nature means values should be interpreted in context of the data scales
/// </remarks>
[SkipLocalsInit]
public sealed class Covar : AbstractBase
{
private readonly int Period;
private readonly CircularBuffer _xValues;
private readonly CircularBuffer _yValues;
private const int MinimumPoints = 2;
/// <param name="period">The number of points to consider for covariance calculation.</param>
/// <exception cref="ArgumentOutOfRangeException">Thrown when period is less than 2.</exception>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public Covar(int period)
{
if (period < MinimumPoints)
{
throw new ArgumentOutOfRangeException(nameof(period),
"Period must be greater than or equal to 2 for covariance calculation.");
}
Period = period;
WarmupPeriod = MinimumPoints;
_xValues = new CircularBuffer(period);
_yValues = new CircularBuffer(period);
Name = $"Covar(period={period})";
Init();
}
/// <param name="source">The data source object that publishes updates.</param>
/// <param name="period">The number of points to consider for covariance calculation.</param>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public Covar(object source, int period) : this(period)
{
var pubEvent = source.GetType().GetEvent("Pub");
pubEvent?.AddEventHandler(source, new ValueSignal(Sub));
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public override void Init()
{
base.Init();
_xValues.Clear();
_yValues.Clear();
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
protected override void ManageState(bool isNew)
{
if (isNew)
{
_lastValidValue = Input.Value;
_index++;
}
}
[MethodImpl(MethodImplOptions.AggressiveInlining | MethodImplOptions.AggressiveOptimization)]
private static double CalculateMean(ReadOnlySpan<double> values)
{
double sum = 0;
for (int i = 0; i < values.Length; i++)
{
sum += values[i];
}
return sum / values.Length;
}
[MethodImpl(MethodImplOptions.AggressiveInlining | MethodImplOptions.AggressiveOptimization)]
private static double CalculateCovariance(ReadOnlySpan<double> xValues, ReadOnlySpan<double> yValues, double xMean, double yMean)
{
double covariance = 0;
for (int i = 0; i < xValues.Length; i++)
{
covariance += (xValues[i] - xMean) * (yValues[i] - yMean);
}
return covariance / xValues.Length;
}
[MethodImpl(MethodImplOptions.AggressiveInlining | MethodImplOptions.AggressiveOptimization)]
protected override double Calculation()
{
ManageState(Input.IsNew);
_xValues.Add(Input.Value, Input.IsNew);
_yValues.Add(Input2.Value, Input.IsNew);
double covariance = 0;
if (_xValues.Count >= MinimumPoints && _yValues.Count >= MinimumPoints)
{
ReadOnlySpan<double> xValues = _xValues.GetSpan();
ReadOnlySpan<double> yValues = _yValues.GetSpan();
double xMean = CalculateMean(xValues);
double yMean = CalculateMean(yValues);
covariance = CalculateCovariance(xValues, yValues, xMean, yMean);
}
IsHot = _xValues.Count >= Period && _yValues.Count >= Period;
return covariance;
}
}
lib/statistics/Kendall.cs
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using System.Runtime.CompilerServices;
namespace QuanTAlib;
/// <summary>
/// KENDALL: Kendall's Rank Correlation Coefficient (Tau)
/// A nonparametric measure that evaluates the degree of similarity between two sets
/// of rankings by analyzing concordant and discordant pairs. Unlike Spearman correlation,
/// Kendall's tau measures the ordinal association between two variables.
/// </summary>
/// <remarks>
/// The Kendall calculation process:
/// 1. Compares each pair of observations
/// 2. Counts concordant and discordant pairs
/// 3. Handles ties in both variables
///
/// Key characteristics:
/// - Measures ordinal association
/// - Range: -1 to +1
/// - Robust to outliers
/// - More intuitive probabilistic interpretation
/// - Less sensitive to error than Spearman
///
/// Formula:
/// τ = (nc - nd) / sqrt((n0 - n1)(n0 - n2))
/// where:
/// nc = number of concordant pairs
/// nd = number of discordant pairs
/// n0 = n(n-1)/2
/// n1 = sum(u(u-1)/2) for ties in x
/// n2 = sum(v(v-1)/2) for ties in y
///
/// Market Applications:
/// - Rank correlation analysis
/// - Portfolio diversification
/// - Risk assessment
/// - Market trend analysis
/// - Pattern recognition
///
/// Sources:
/// https://en.wikipedia.org/wiki/Kendall_rank_correlation_coefficient
/// "Rank Correlation Methods" - Maurice G. Kendall
///
/// Note: More robust to outliers and errors than other correlation measures
/// </remarks>
[SkipLocalsInit]
public sealed class Kendall : AbstractBase
{
private readonly int Period;
private readonly CircularBuffer _xValues;
private readonly CircularBuffer _yValues;
private const double Epsilon = 1e-10;
private const int MinimumPoints = 2;
/// <param name="period">The number of points to consider for Kendall correlation calculation.</param>
/// <exception cref="ArgumentOutOfRangeException">Thrown when period is less than 2.</exception>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public Kendall(int period)
{
if (period < MinimumPoints)
{
throw new ArgumentOutOfRangeException(nameof(period),
"Period must be greater than or equal to 2 for Kendall correlation calculation.");
}
Period = period;
WarmupPeriod = MinimumPoints;
_xValues = new CircularBuffer(period);
_yValues = new CircularBuffer(period);
Name = $"Kendall(period={period})";
Init();
}
/// <param name="source">The data source object that publishes updates.</param>
/// <param name="period">The number of points to consider for Kendall correlation calculation.</param>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public Kendall(object source, int period) : this(period)
{
var pubEvent = source.GetType().GetEvent("Pub");
pubEvent?.AddEventHandler(source, new ValueSignal(Sub));
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public override void Init()
{
base.Init();
_xValues.Clear();
_yValues.Clear();
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
protected override void ManageState(bool isNew)
{
if (isNew)
{
_lastValidValue = Input.Value;
_index++;
}
}
[MethodImpl(MethodImplOptions.AggressiveInlining | MethodImplOptions.AggressiveOptimization)]
private static (int concordant, int discordant, int tiesX, int tiesY) CountPairs(ReadOnlySpan<double> x, ReadOnlySpan<double> y)
{
int n = x.Length;
int concordant = 0;
int discordant = 0;
int tiesX = 0;
int tiesY = 0;
for (int i = 0; i < n - 1; i++)
{
if (double.IsNaN(x[i]) || double.IsNaN(y[i])) continue;
for (int j = i + 1; j < n; j++)
{
if (double.IsNaN(x[j]) || double.IsNaN(y[j])) continue;
double xDiff = x[i] - x[j];
double yDiff = y[i] - y[j];
if (Math.Abs(xDiff) < Epsilon && Math.Abs(yDiff) < Epsilon)
{
tiesX++;
tiesY++;
}
else if (Math.Abs(xDiff) < Epsilon)
{
tiesX++;
}
else if (Math.Abs(yDiff) < Epsilon)
{
tiesY++;
}
else
{
int xSign = xDiff > 0 ? 1 : -1;
int ySign = yDiff > 0 ? 1 : -1;
if (xSign == ySign)
{
concordant++;
}
else
{
discordant++;
}
}
}
}
return (concordant, discordant, tiesX, tiesY);
}
[MethodImpl(MethodImplOptions.AggressiveInlining | MethodImplOptions.AggressiveOptimization)]
protected override double Calculation()
{
ManageState(Input.IsNew);
_xValues.Add(Input.Value, Input.IsNew);
_yValues.Add(Input2.Value, Input.IsNew);
double correlation = 0;
if (_xValues.Count >= MinimumPoints && _yValues.Count >= MinimumPoints)
{
ReadOnlySpan<double> xValues = _xValues.GetSpan();
ReadOnlySpan<double> yValues = _yValues.GetSpan();
var (concordant, discordant, tiesX, tiesY) = CountPairs(xValues, yValues);
int n = xValues.Length;
int n0 = (n * (n - 1)) / 2;
// Calculate denominator considering ties
double denominator = Math.Sqrt((n0 - tiesX) * (n0 - tiesY));
if (denominator > Epsilon)
{
correlation = (concordant - discordant) / denominator;
}
}
IsHot = _xValues.Count >= Period && _yValues.Count >= Period;
return correlation;
}
}
lib/statistics/Spearman.cs
+224
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@@ -0,0 +1,224 @@
using System.Runtime.CompilerServices;
namespace QuanTAlib;
/// <summary>
/// SPEARMAN: Spearman's Rank Correlation Coefficient
/// A nonparametric measure of rank correlation that assesses the monotonic relationship
/// between two variables. Unlike Pearson correlation, Spearman correlation evaluates
/// the relationship based on ranked values rather than raw data.
/// </summary>
/// <remarks>
/// The Spearman calculation process:
/// 1. Ranks both sets of values
/// 2. Calculates correlation between ranks
/// 3. Handles ties by averaging ranks
///
/// Key characteristics:
/// - Resistant to outliers
/// - Detects monotonic relationships
/// - Range: -1 to +1
/// - Distribution-free measure
/// - Handles non-linear relationships
///
/// Formula:
/// ρ = Cov(rank(X), rank(Y)) / (σrank(X) * σrank(Y))
/// where:
/// X, Y = variables
/// rank() = ranking function
/// Cov = covariance
/// σ = standard deviation
///
/// Market Applications:
/// - Technical analysis
/// - Risk assessment
/// - Market correlation studies
/// - Trend analysis
/// - Pattern recognition
///
/// Sources:
/// https://en.wikipedia.org/wiki/Spearman%27s_rank_correlation_coefficient
/// "Nonparametric Statistics for Non-Statisticians" - Gregory W. Corder
///
/// Note: More robust to outliers than Pearson correlation
/// </remarks>
[SkipLocalsInit]
public sealed class Spearman : AbstractBase
{
private readonly int Period;
private readonly CircularBuffer _xValues;
private readonly CircularBuffer _yValues;
private readonly CircularBuffer _xRanks;
private readonly CircularBuffer _yRanks;
private const double Epsilon = 1e-10;
private const int MinimumPoints = 2;
/// <param name="period">The number of points to consider for Spearman correlation calculation.</param>
/// <exception cref="ArgumentOutOfRangeException">Thrown when period is less than 2.</exception>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public Spearman(int period)
{
if (period < MinimumPoints)
{
throw new ArgumentOutOfRangeException(nameof(period),
"Period must be greater than or equal to 2 for Spearman correlation calculation.");
}
Period = period;
WarmupPeriod = MinimumPoints;
_xValues = new CircularBuffer(period);
_yValues = new CircularBuffer(period);
_xRanks = new CircularBuffer(period);
_yRanks = new CircularBuffer(period);
Name = $"Spearman(period={period})";
Init();
}
/// <param name="source">The data source object that publishes updates.</param>
/// <param name="period">The number of points to consider for Spearman correlation calculation.</param>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public Spearman(object source, int period) : this(period)
{
var pubEvent = source.GetType().GetEvent("Pub");
pubEvent?.AddEventHandler(source, new ValueSignal(Sub));
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public override void Init()
{
base.Init();
_xValues.Clear();
_yValues.Clear();
_xRanks.Clear();
_yRanks.Clear();
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
protected override void ManageState(bool isNew)
{
if (isNew)
{
_lastValidValue = Input.Value;
_index++;
}
}
[MethodImpl(MethodImplOptions.AggressiveInlining | MethodImplOptions.AggressiveOptimization)]
private static double[] CalculateRanks(ReadOnlySpan<double> values)
{
int n = values.Length;
var pairs = new (double value, int index)[n];
for (int i = 0; i < n; i++)
{
pairs[i] = double.IsNaN(values[i]) ? (double.NaN, i) : (values[i], i);
}
// Sort non-NaN values
var validPairs = pairs.Where(p => !double.IsNaN(p.value)).OrderBy(p => p.value).ToArray();
var ranks = new double[n];
Array.Fill(ranks, double.NaN);
for (int i = 0; i < validPairs.Length;)
{
int j = i;
// Find ties
while (j < validPairs.Length - 1 && Math.Abs(validPairs[j].value - validPairs[j + 1].value) < Epsilon)
{
j++;
}
// Average rank for ties
double rank = (i + j) / 2.0 + 1;
for (int k = i; k <= j; k++)
{
ranks[validPairs[k].index] = rank;
}
i = j + 1;
}
return ranks;
}
[MethodImpl(MethodImplOptions.AggressiveInlining | MethodImplOptions.AggressiveOptimization)]
private static double CalculateCovariance(CircularBuffer xBuffer, CircularBuffer yBuffer, double xMean, double yMean)
{
var xSpan = xBuffer.GetSpan();
var ySpan = yBuffer.GetSpan();
double covariance = 0;
int count = 0;
for (int i = 0; i < xSpan.Length; i++)
{
if (!double.IsNaN(xSpan[i]) && !double.IsNaN(ySpan[i]))
{
covariance += (xSpan[i] - xMean) * (ySpan[i] - yMean);
count++;
}
}
return count > 0 ? covariance / count : double.NaN;
}
[MethodImpl(MethodImplOptions.AggressiveInlining | MethodImplOptions.AggressiveOptimization)]
private static double CalculateStandardDeviation(CircularBuffer buffer, double mean)
{
var span = buffer.GetSpan();
double sumSquaredDeviations = 0;
int count = 0;
for (int i = 0; i < span.Length; i++)
{
if (!double.IsNaN(span[i]))
{
double deviation = span[i] - mean;
sumSquaredDeviations += deviation * deviation;
count++;
}
}
return count > 0 ? Math.Sqrt(sumSquaredDeviations / count) : double.NaN;
}
[MethodImpl(MethodImplOptions.AggressiveInlining | MethodImplOptions.AggressiveOptimization)]
protected override double Calculation()
{
ManageState(Input.IsNew);
_xValues.Add(Input.Value, Input.IsNew);
_yValues.Add(Input2.Value, Input.IsNew);
double correlation = 0;
if (_xValues.Count >= MinimumPoints && _yValues.Count >= MinimumPoints)
{
// Convert values to ranks
var xRanks = CalculateRanks(_xValues.GetSpan());
var yRanks = CalculateRanks(_yValues.GetSpan());
// Store ranks in buffers for statistical calculations
_xRanks.Clear();
_yRanks.Clear();
for (int i = 0; i < xRanks.Length; i++)
{
_xRanks.Add(xRanks[i], true);
_yRanks.Add(yRanks[i], true);
}
// Use CircularBuffer's optimized Average() method
double xMean = _xRanks.Average();
double yMean = _yRanks.Average();
if (!double.IsNaN(xMean) && !double.IsNaN(yMean))
{
double covariance = CalculateCovariance(_xRanks, _yRanks, xMean, yMean);
double xStdDev = CalculateStandardDeviation(_xRanks, xMean);
double yStdDev = CalculateStandardDeviation(_yRanks, yMean);
if (!double.IsNaN(covariance) && xStdDev > Epsilon && yStdDev > Epsilon)
{
correlation = covariance / (xStdDev * yStdDev);
}
}
}
IsHot = _xValues.Count >= Period && _yValues.Count >= Period;
return correlation;
}
}
lib/statistics/_list.md
+25 -31
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@@ -1,32 +1,26 @@
# Statistics
# Statistics indicators
Done: 21, Todo: 2
Statistical functions and indicators for financial analysis.
## Implemented
- [Beta](Beta.cs) - Beta coefficient measuring volatility relative to market
- [Corr](Corr.cs) - Correlation coefficient between two series
- [Curvature](Curvature.cs) - Curvature of a time series
- [Entropy](Entropy.cs) - Information entropy of a series
- [Hurst](Hurst.cs) - Hurst exponent for trend strength
- [Kurtosis](Kurtosis.cs) - Kurtosis measuring tail extremity
- [Max](Max.cs) - Maximum value over period
- [Median](Median.cs) - Median value over period
- [Min](Min.cs) - Minimum value over period
- [Mode](Mode.cs) - Mode (most frequent value)
- [Percentile](Percentile.cs) - Percentile rank calculation
- [Skew](Skew.cs) - Skewness measuring distribution asymmetry
- [Slope](Slope.cs) - Linear regression slope
- [Stddev](Stddev.cs) - Standard deviation
- [Theil](Theil.cs) - Theil's U statistics for forecast accuracy
- [Tsf](Tsf.cs) - Time series forecast
- [Variance](Variance.cs) - Statistical variance
- [Zscore](Zscore.cs) - Z-score standardization
## Planned
- Cointegration - Test for cointegrated series
- Granger - Granger causality test
- Jarque-Bera - Normality test
- Kendall - Kendall rank correlation
- Spearman - Spearman rank correlation
✔️ BETA - Beta coefficient measuring volatility relative to market
✔️ CORR - Correlation coefficient between two series
✔️ COVAR - Covariance between two series
✔️ CURVATURE - Curvature of a time series
✔️ ENTROPY - Information entropy of a series
✔️ HURST - Hurst exponent for trend strength
✔️ KENDALL - Kendall rank correlation
✔️ KURTOSIS - Kurtosis measuring tail extremity
✔️ MAX - Maximum value over period
✔️ MEDIAN - Median value over period
✔️ MIN - Minimum value over period
✔️ MODE - Mode (most frequent value)
✔️ PERCENTILE - Percentile rank calculation
✔️ SKEW - Skewness measuring distribution asymmetry
✔️ SLOPE - Linear regression slope
✔️ SPEARMAN - Spearman rank correlation
✔️ STDDEV - Standard deviation
✔️ THEIL - Theil's U statistics for forecast accuracy
✔️ TSF - Time series forecast
✔️ VARIANCE - Statistical variance
✔️ ZSCORE - Z-score standardization
COINTEGRATION - Test for cointegrated series
GRANGER - Granger causality test
lib/volatility/_list.md
+7 -7
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@@ -1,5 +1,5 @@
# Volatility indicators
Done: 25, Todo: 10
Done: 31, Todo: 4
✔️ ADR - Average Daily Range
✔️ AP - Andrew's Pitchfork
@@ -17,22 +17,22 @@ Done: 25, Todo: 10
✔️ GKV - Garman-Klass Volatility
✔️ HLV - High-Low Volatility
✔️ HV - Historical Volatility
*ICH - Ichimoku Cloud (Conversion, Base, Leading Span A, Leading Span B, Lagging Span)
✔️ *JVOLTY - Jurik Volatility (Jvolty, Upper band, Lower band)
*KC - Keltner Channels (Upper, Middle, Lower)
✔️ JVOLTY - Jurik Volatility (Jvolty, Upper band, Lower band)
✔️ NATR - Normalized Average True Range
✔️ PCH - Price Channel Indicator
*PSAR - Parabolic Stop and Reverse (Value, Trend)
✔️ PV - Parkinson Volatility
✔️ RSV - Rogers-Satchell Volatility
✔️ RV - Realized Volatility
✔️ RVI - Relative Volatility Index
*STARC - Starc Bands (Upper, Middle, Lower)
✔️ SV - Stochastic Volatility
✔️ TR - True Range
✔️ UI - Ulcer Index
✔️ *VC - Volatility Cone (Mean, Upper Bound, Lower Bound)
✔️ VC - Volatility Cone (Mean, Upper Bound, Lower Bound)
✔️ VOV - Volatility of Volatility
✔️ VR - Volatility Ratio
✔️ *VS - Volatility Stop (Long Stop, Short Stop)
✔️ YZV - Yang-Zhang Volatility
ICH - Ichimoku Cloud (Conversion, Base, Leading Span A, Leading Span B, Lagging Span)
KC - Keltner Channels (Upper, Middle, Lower)
PSAR - Parabolic Stop and Reverse (Value, Trend)
STARC - Starc Bands (Upper, Middle, Lower)