RSI vs Wilder's RSI Calculation Problems

Question

I am having trouble getting a smoothed RSI. The below picture is from freestockcharts.com. The calculation uses this code.

public static double CalculateRsi(IEnumerable<double> closePrices)
{
    var prices = closePrices as double[] ?? closePrices.ToArray();

    double sumGain = 0;
    double sumLoss = 0;
    for (int i = 1; i < prices.Length; i++)
    {
        var difference = prices[i] - prices[i - 1];
        if (difference >= 0)
        {
            sumGain += difference;
        }
        else
        {
            sumLoss -= difference;
        }
    }

    if (sumGain == 0) return 0;
    if (Math.Abs(sumLoss) < Tolerance) return 100;

    var relativeStrength = sumGain / sumLoss;

    return 100.0 - (100.0 / (1 + relativeStrength));
}

https://stackoverflow.com/questions/...th-index-using-some-programming-language-js-c

This seems to be the pure RSI with no smoothing. How does a smoothed RSI get calculated? I have tried changing it to fit the definitions of the these two sites however the output was not correct. It was barely smoothed.

(I don't have enough rep to post links)

tc2000 -> Indicators -> RSI_and_Wilder_s_RSI (Wilder's smoothing = Previous MA value + (1/n periods * (Close - Previous MA)))

priceactionlab -> wilders-cutlers-and-harris-relative-strength-index (RS = EMA(Gain(n), n)/EMA(Loss(n), n))

Can someone actually do the calculation with some sample data?

Wilder's RSI vs RSI

Answer 1

Some trading software's script to calculate RSI:

LC:=REF(CLOSE,1);
RSI1:SMA(MAX(CLOSE-LC,0),N1,1)/SMA(ABS(CLOSE-LC),N1,1)*100;
RSI2:SMA(MAX(CLOSE-LC,0),N2,1)/SMA(ABS(CLOSE-LC),N2,1)*100;
RSI3:SMA(MAX(CLOSE-LC,0),N3,1)/SMA(ABS(CLOSE-LC),N3,1)*100;

It use SMA to smooth, I find EMA is better, see https://stackoverflow.com/a/79049176/27601242

Answer 2

You can't get accurate values without buffers / global variables to store data.

This is a smoothed indicator, meaning it doesn't only use 14 bars but ALL THE BARS: Here's a step by step article with working and verified source codes generating exactly the same values if prices and number of available bars are the same, of course (you only need to load the price data from your source):

Tested and verified:

using System;
using System.Data;
using System.Globalization;

namespace YourNameSpace
  {
   class PriceEngine
      {
        public static DataTable data;
        public static double[] positiveChanges;
        public static double[] negativeChanges;
        public static double[] averageGain;
        public static double[] averageLoss;
        public static double[] rsi;
        
        public static double CalculateDifference(double current_price, double previous_price)
          {
              return current_price - previous_price;
          }

        public static double CalculatePositiveChange(double difference)
          {
              return difference > 0 ? difference : 0;
          }

        public static double CalculateNegativeChange(double difference)
          {
              return difference < 0 ? difference * -1 : 0;
          }

        public static void CalculateRSI(int rsi_period, int price_index = 5)
          {
              for(int i = 0; i < PriceEngine.data.Rows.Count; i++)
              {
                  double current_difference = 0.0;
                  if (i > 0)
                  {
                      double previous_close = Convert.ToDouble(PriceEngine.data.Rows[i-1].Field<string>(price_index));
                      double current_close = Convert.ToDouble(PriceEngine.data.Rows[i].Field<string>(price_index));
                      current_difference = CalculateDifference(current_close, previous_close);
                  }
                  PriceEngine.positiveChanges[i] = CalculatePositiveChange(current_difference);
                  PriceEngine.negativeChanges[i] = CalculateNegativeChange(current_difference);

                  if(i == Math.Max(1,rsi_period))
                  {
                      double gain_sum = 0.0;
                      double loss_sum = 0.0;
                      for(int x = Math.Max(1,rsi_period); x > 0; x--)
                      {
                          gain_sum += PriceEngine.positiveChanges[x];
                          loss_sum += PriceEngine.negativeChanges[x];
                      }

                      PriceEngine.averageGain[i] = gain_sum / Math.Max(1,rsi_period);
                      PriceEngine.averageLoss[i] = loss_sum / Math.Max(1,rsi_period);

                  }else if (i > Math.Max(1,rsi_period))
                  {
                      PriceEngine.averageGain[i] = ( PriceEngine.averageGain[i-1]*(rsi_period-1) + PriceEngine.positiveChanges[i]) / Math.Max(1, rsi_period);
                      PriceEngine.averageLoss[i] = ( PriceEngine.averageLoss[i-1]*(rsi_period-1) + PriceEngine.negativeChanges[i]) / Math.Max(1, rsi_period);
                      PriceEngine.rsi[i] = PriceEngine.averageLoss[i] == 0 ? 100 : PriceEngine.averageGain[i] == 0 ? 0 : Math.Round(100 - (100 / (1 + PriceEngine.averageGain[i] / PriceEngine.averageLoss[i])), 5);
                  }
              }
          }
          
        public static void Launch()
          {
            PriceEngine.data = new DataTable();            
            //load {date, time, open, high, low, close} values in PriceEngine.data (6th column (index #5) = close price) here
            
            positiveChanges = new double[PriceEngine.data.Rows.Count];
            negativeChanges = new double[PriceEngine.data.Rows.Count];
            averageGain = new double[PriceEngine.data.Rows.Count];
            averageLoss = new double[PriceEngine.data.Rows.Count];
            rsi = new double[PriceEngine.data.Rows.Count];
            
            CalculateRSI(14);
          }
          
      }
  }

For detailed step-by-step instructions, I wrote a lengthy article, you can check it here: https://turmanauli.medium.com/a-step-by-step-guide-for-calculating-reliable-rsi-values-programmatically-a6a604a06b77

P.S. functions only work for simple indicators (Simple Moving Average), even Exponential Moving Average, Average True Range absolutely require global variables to store previous values.

Answer 3

In order to calculate the RSI, you need a period to calculate it with. As noted on Wikipedia, 14 is used quite often.

So the calculation steps would be as follows:

Period 1 - 13, RSI = 0

Period 14:

AverageGain = TotalGain / PeriodCount;
AverageLoss = TotalLoss / PeriodCount;
RS = AverageGain / AverageLoss;
RSI = 100 - 100 / (1 + RS);

Period 15 - to period (N):

if (Period(N)Change > 0
  AverageGain(N) = ((AverageGain(N - 1) * (PeriodCount - 1)) + Period(N)Change) / PeriodCount;
else
  AverageGain(N) = (AverageGain(N - 1) * (PeriodCount - 1)) / PeriodCount;

if (this.Change < 0)
  AverageLoss(N) = ((AverageLoss(N - 1) * (PeriodCount - 1)) + Math.Abs(Period(N)Change)) / PeriodCount;
else
  AverageLoss(N) = (AverageLoss(N - 1) * (PeriodCount - 1)) / PeriodCount;

RS = AverageGain / AverageLoss;
RSI = 100 - (100 / (1 + RS));

Thereafter, to smooth the values, you need to apply a moving average of a certain period to your RSI values. To do that, traverse your RSI values from the last index to the first and calculate your average for the current period based on the preceding x smoothing periods.

Once done, just reverse the list of values to get the expected order:

List<double> SmoothedRSI(IEnumerable<double> rsiValues, int smoothingPeriod)
{
  if (rsiValues.Count() <= smoothingPeriod)
    throw new Exception("Smoothing period too large or too few RSI values passed.");

  List<double> results = new List<double>();
  List<double> reversedRSIValues = rsiValues.Reverse().ToList();

  for (int i = 1; i < reversedRSIValues.Count() - smoothingPeriod - 1; i++)
    results.Add(reversedRSIValues.Subset(i, i + smoothingPeriod).Average());

  return results.Reverse().ToList();
}

The Subset method is just a simple extension method as follows:

public static List<double> Subset(this List<double> values, int start, int end)
{
  List<double> results = new List<double>();

  for (int i = start; i <= end; i++)
    results.Add(values[i]);

  return results;
}

Disclaimer, I did not test the code, but it should give you an idea of how the smoothing is applied.