What is incorrect in my autocorrelation computation? [closed]

In the following source codes, Python and R are giving the same result.

However, C# is giving an incorrect result.

How can I fix the C# code?

Input data:

[1.0, 1.25, 1.5, 1.75, 2.0, 2.25, 3.33]

Python code:

import numpy as npdata = np.array([1.0, 1.25, 1.5, 1.75, 2.0, 2.25, 3.33])n = len(data)mean = np.mean(data)autocorrelations = {}for lag in range(1, n):    cov = np.sum((data[:-lag] - mean) * (data[lag:] - mean))    var = np.sum((data - mean) ** 2)    autocorrelations[lag] = cov / varprint(autocorrelations)

Output:

{1: 0.3907255328740364, 2: 0.13718688954560562, 3: -0.08148897368528898, 4: -0.24787066676987946, 5: -0.3445267996593978, 6: -0.3540259823050758}

R code:

values <- c(1.0, 1.25, 1.5, 1.75, 2.0, 2.25, 3.33)autocorrelations <- sapply(1:(length(values)-1), function(lag) {  acf(values, lag.max=lag, plot=FALSE)$acf[lag + 1]})autocorrelations

Output:

0.39072553  0.13718689 -0.08148897 -0.24787067 -0.34452680 -0.35402598

C# code:

using MathNet.Numerics.Statistics;using System;using System.Collections.Generic;using System.Linq;namespace AutoCorrUsingMathNet{    public class Statistics    {        private List<double> data_;        public Statistics(List<double> data)        {            if (data == null || !data.Any())                throw new ArgumentException("Data cannot be null or empty.", nameof(data));            data_ = data;        }                public double AutocorrelationCoeff(int lag)        {            if (lag >= data_.Count || lag < 0)                throw new ArgumentException("Lag is out of range.", nameof(lag));            var laggedData = data_.Skip(lag).ToList();            var originalData = data_.Take(data_.Count - lag).ToList();            return Correlation.Pearson(originalData, laggedData);        }        public (List<double>, List<double>) AutoCorrelationPoints(double thresholdMin = 0.0001, double thresholdMax = 0.9999, double numLag = 1000)        {            List<double> tau = new List<double>();            List<double> autocorrelationValues = new List<double>();            for (int lag = 0; lag < numLag; lag++)            {                double autoCorr = AutocorrelationCoeff(lag);                if (thresholdMin < autoCorr && autoCorr < thresholdMax)                {                    tau.Add(lag);                    autocorrelationValues.Add(autoCorr);                }            }            return (tau, autocorrelationValues);        }    }    public class Program    {        static void Main(string[] args)        {            List<double> dataList = new List<double>(new double[] { 1.0, 1.25, 1.5, 1.75, 2.0, 2.25, 3.33 });            List<double> autoCorrExpectedList = new List<double>(new double[] { 0.3907, 0.1372, -0.0029, -0.2479 });            Statistics stats = new Statistics(dataList);            var autoCorr = stats.AutoCorrelationPoints(numLag: dataList.Count - 1);            List<double> lagList = autoCorr.Item1;            List<double> autoCorrActualList = autoCorr.Item2;            foreach (var item in autoCorrActualList)            {                Console.WriteLine(item);            }            Console.ReadKey();        }    }}

Output:

0.9374115462038420.9287843240596310.9260849979667670.940797041158867