QuanTAlib/lib/statistics/covariance/Covariance.Validation.Tests.cs

namespace QuanTAlib.Tests;

public class CovarianceValidationTests
{
    [Fact]
    public void Covariance_Matches_ManualCalculation()
    {
        // Arrange
        const int period = 10;
        var cov = new Covariance(period, isPopulation: false);
        var gbmX = new GBM(startPrice: 100, mu: 0.05, sigma: 0.2, seed: 123);
        var gbmY = new GBM(startPrice: 100, mu: 0.05, sigma: 0.2, seed: 456);

        double[] x = new double[100];
        double[] y = new double[100];
        for (int i = 0; i < 100; i++)
        {
            x[i] = gbmX.Next().Close;
            y[i] = gbmY.Next().Close;
            cov.Update(x[i], y[i]);

            if (i >= period - 1)
            {
                // Manual calculation for last 'period' items
                double sumX = 0;
                double sumY = 0;
                for (int j = 0; j < period; j++)
                {
                    sumX += x[i - j];
                    sumY += y[i - j];
                }
                double meanX = sumX / period;
                double meanY = sumY / period;

                double sumProd = 0;
                for (int j = 0; j < period; j++)
                {
                    sumProd += (x[i - j] - meanX) * (y[i - j] - meanY);
                }

                double expected = sumProd / (period - 1);
                Assert.Equal(expected, cov.Last.Value, precision: 8);
            }
        }
    }

    [Fact]
    public void Covariance_Population_Matches_ManualCalculation()
    {
        // Arrange
        int period = 10;
        var cov = new Covariance(period, isPopulation: true);
        var gbmX = new GBM(startPrice: 100, mu: 0.05, sigma: 0.2, seed: 456);
        var gbmY = new GBM(startPrice: 100, mu: 0.05, sigma: 0.2, seed: 789);

        double[] x = new double[100];
        double[] y = new double[100];
        for (int i = 0; i < 100; i++)
        {
            x[i] = gbmX.Next().Close;
            y[i] = gbmY.Next().Close;
            cov.Update(x[i], y[i]);

            if (i >= period - 1)
            {
                // Manual calculation for last 'period' items
                double sumX = 0;
                double sumY = 0;
                for (int j = 0; j < period; j++)
                {
                    sumX += x[i - j];
                    sumY += y[i - j];
                }
                double meanX = sumX / period;
                double meanY = sumY / period;

                double sumProd = 0;
                for (int j = 0; j < period; j++)
                {
                    sumProd += (x[i - j] - meanX) * (y[i - j] - meanY);
                }

                double expected = sumProd / period;
                Assert.Equal(expected, cov.Last.Value, precision: 8);
            }
        }
    }
}