从前一天开始的EMA的指数移动平均线问题

Question

简要说明：

我在下面得到了简单的移动平均线和指数移动平均线公式。第一支蜡烛的EMA（前一天）差异很大。那是因为我没有前一天EMA的数据，并且此公式使用了SMA。对应的行：yesterdaysEMA = CalculateSimpleMovingAverage(numberOfDays, historicalDataList);。我不太确定Binance / TradingView如何获取第一个值。

更多详细信息：

我正在为下面图片中随附的蜡烛计算EMA（5）。

Binance的实际值：

Candle 1: EMA(5) = 0.020547
Candle 2: EMA(5) = 0.020558
Candle 3: EMA(5) = 0.020529
Candle 4: EMA(5) = 0.020506
Candle 5: EMA(5) = 0.020441

如果我手动将yesterdaysEMA设置为与币安值0.020580相对应，我将收到以下值：

Candle 1: EMA(5) = 0.0205466666666666666666666667
Candle 2: EMA(5) = 0.0205577777777777777777777778
Candle 3: EMA(5) = 0.0205285185185185185185185185
Candle 4: EMA(5) = 0.0205056790123456790123456790
Candle 5: EMA(5) = 0.0204404526748971193415637860

这使我使用的公式正确。通过我的公式计算出的yesterdaysEMA的SMA为0.02046000。与0.020580相比，有很大的不同。

问题是如何用币安的第一个蜡烛EMA（5）数据同步公式？

EDIT：如果没有前一天EMA的数据，我看到Binance正在使用收盘价。这让我想知道应该计算多少支蜡烛，这样我才能接近它们的值。

数据（TRX / USDT-30分钟间隔）：

Open time (UTC): 2/23/2020 9:30:00 PM
Close time (UTC): 2/23/2020 9:59:59 PM
High: 0.02091000
Low: 0.02079000
Open: 0.02091000
Close: 0.02083000

Open time (UTC): 2/23/2020 10:00:00 PM
Close time (UTC): 2/23/2020 10:29:59 PM
High: 0.02086000
Low: 0.02076000
Open: 0.02084000
Close: 0.02077000

Open time (UTC): 2/23/2020 10:30:00 PM
Close time (UTC): 2/23/2020 10:59:59 PM
High: 0.02107000
Low: 0.02076000
Open: 0.02076000
Close: 0.02101000

Open time (UTC): 2/23/2020 11:00:00 PM
Close time (UTC): 2/23/2020 11:29:59 PM
High: 0.02124000
Low: 0.02100000
Open: 0.02101000
Close: 0.02122000

Open time (UTC): 2/23/2020 11:30:00 PM
Close time (UTC): 2/23/2020 11:59:59 PM
High: 0.02142000
Low: 0.02120000
Open: 0.02122000
Close: 0.02133000

Open time (UTC): 2/24/2020 12:00:00 AM
Close time (UTC): 2/24/2020 12:29:59 AM
High: 0.02136000
Low: 0.02117000
Open: 0.02133000
Close: 0.02131000

Open time (UTC): 2/24/2020 12:30:00 AM
Close time (UTC): 2/24/2020 12:59:59 AM
High: 0.02134000
Low: 0.02116000
Open: 0.02131000
Close: 0.02122000

Open time (UTC): 2/24/2020 1:00:00 AM
Close time (UTC): 2/24/2020 1:29:59 AM
High: 0.02123000
Low: 0.02107000
Open: 0.02122000
Close: 0.02112000

Open time (UTC): 2/24/2020 1:30:00 AM
Close time (UTC): 2/24/2020 1:59:59 AM
High: 0.02113000
Low: 0.02098000
Open: 0.02112000
Close: 0.02100000

Open time (UTC): 2/24/2020 2:00:00 AM
Close time (UTC): 2/24/2020 2:29:59 AM
High: 0.02112000
Low: 0.02096000
Open: 0.02101000
Close: 0.02099000

Open time (UTC): 2/24/2020 2:30:00 AM
Close time (UTC): 2/24/2020 2:59:59 AM
High: 0.02099000
Low: 0.02011000
Open: 0.02098000
Close: 0.02045000

Open time (UTC): 2/24/2020 3:00:00 AM
Close time (UTC): 2/24/2020 3:29:59 AM
High: 0.02058000
Low: 0.02035000
Open: 0.02047000
Close: 0.02041000

Open time (UTC): 2/24/2020 3:30:00 AM
Close time (UTC): 2/24/2020 3:59:59 AM
High: 0.02061000
Low: 0.02040000
Open: 0.02041000
Close: 0.02055000

Open time (UTC): 2/24/2020 4:00:00 AM
Close time (UTC): 2/24/2020 4:29:59 AM
High: 0.02055000
Low: 0.02040000
Open: 0.02054000
Close: 0.02044000

Open time (UTC): 2/24/2020 4:30:00 AM
Close time (UTC): 2/24/2020 4:59:59 AM
High: 0.02058000
Low: 0.02042000
Open: 0.02044000
Close: 0.02057000

Open time (UTC): 2/24/2020 5:00:00 AM
Close time (UTC): 2/24/2020 5:29:59 AM
High: 0.02056000
Low: 0.02046000
Open: 0.02056000
Close: 0.02048000

Open time (UTC): 2/24/2020 5:30:00 AM
Close time (UTC): 2/24/2020 5:59:59 AM
High: 0.02061000
Low: 0.02047000
Open: 0.02048000
Close: 0.02058000

Open time (UTC): 2/24/2020 6:00:00 AM
Close time (UTC): 2/24/2020 6:29:59 AM
High: 0.02060000
Low: 0.02047000
Open: 0.02060000
Close: 0.02047000

Open time (UTC): 2/24/2020 6:30:00 AM
Close time (UTC): 2/24/2020 6:59:59 AM
High: 0.02054000
Low: 0.02039000
Open: 0.02048000
Close: 0.02046000

Open time (UTC): 2/24/2020 7:00:00 AM
Close time (UTC): 2/24/2020 7:29:59 AM
High: 0.02044000
Low: 0.02019000
Open: 0.02044000
Close: 0.02031000

public class ExponentialMovingAverage
{
    public static decimal CalculateSimpleMovingAverage(int numberOfDays, List<BinanceKline> historicalDataList)
    {
        if (historicalDataList.Count >= numberOfDays)
        {
            decimal sumOfAllOnClose = 0;
            for (int i = 0; i < numberOfDays; i++)
            {
                sumOfAllOnClose = sumOfAllOnClose + historicalDataList[i].Close;
            }

            return sumOfAllOnClose / numberOfDays;
        }
        else
            return 0;
    }

    public static decimal ExponentialMovingAverageFormula(decimal todaysPrice, decimal yesterdaysEMA, decimal numberOfDays)
    {
        decimal multiplier = (2 / (numberOfDays + 1));
        return (todaysPrice - yesterdaysEMA) * multiplier + yesterdaysEMA;
    }

    public static decimal CalculateExponentialMovingAverage(int numberOfDays, List<BinanceKline> historicalDataList)
    {
        decimal yesterdaysEMA = 0;
        if (historicalDataList.Count >= numberOfDays)
        {
            decimal sumOfEMA = 0;
            for (int i = 0; i < numberOfDays; i++)
            {
                if (i == 0)
                {
                    yesterdaysEMA = CalculateSimpleMovingAverage(numberOfDays, historicalDataList);
                }
                decimal eMA = ExponentialMovingAverageFormula(historicalDataList[i].Close, yesterdaysEMA, numberOfDays);
                sumOfEMA += eMA;
                yesterdaysEMA = eMA;
            }

            return sumOfEMA / numberOfDays;
        }
        else
            return 0;
    }
}