火花指数移动平均线 [英] Spark Exponential Moving Average

问题描述

我有一个时间序列定价数据的数据框，带有 ID、日期和价格.

I have a dataframe of timeseries pricing data, with an ID, Date and Price.

我需要计算价格列的指数移动平均线，并将其作为新列添加到数据框中.

I need to compute the Exponential Moving Average for the Price Column, and add it as a new column to the dataframe.

我之前一直在使用 Spark 的窗口函数，它看起来很适合这个用例，但考虑到 EMA 的公式:

I have been using Spark's window functions before, and it looked like a fit for this use case, but given the formula for the EMA:

EMA: {Price - EMA(previous day)} x multiplier + EMA(previous day)

哪里

multiplier = (2 / (Time periods + 1)) //let's assume Time period is 10 days for now

我对如何访问列中的先前计算值感到有些困惑，同时实际上对列进行了窗口化.使用简单的移动平均线，这很简单，因为您需要做的就是在平均窗口中的元素的同时计算一个新列:

I got a bit confused as to how can I access to the previous computed value in the column, while actually window-ing over the column. With a simple moving average, it's simple, since all you need to do is compute a new column while averaging the elements in the window:

var window = Window.partitionBy("ID").orderBy("Date").rowsBetween(-windowSize, Window.currentRow)
dataFrame.withColumn(avg(col("Price")).over(window).alias("SMA"))

但似乎 EMA 有点复杂，因为在每一步我都需要之前的计算值.

But it seems that with EMA its a bit more complicated since at every step I need the previous computed value.

我还查看了 Pyspark 中的加权移动平均线，但我需要一种方法对于 Spark/Scala，以及 10 或 30 天的 EMA.

I have also looked at Weighted moving average in Pyspark but I need an approach for Spark/Scala, and for a 10 or 30 days EMA.

有什么想法吗?

推荐答案

最后，我分析了如何在 pandas 数据帧中实现指数移动平均线.除了我上面描述的递归公式，在任何sql或窗口函数中都很难实现(因为它是递归的)，还有另一个，在他们的问题跟踪器:

In the end, I've analysed how exponential moving average is implemented in pandas dataframes. Besides the recursive formula which I described above, and which is difficult to implement in any sql or window function(because its recursive), there is another one, which is detailed on their issue tracker:

y[t] = (x[t] + (1-a)*x[t-1] + (1-a)^2*x[t-2] + ... + (1-a)^n*x[t-n]) /
       ((1-a)^0 + (1-a)^1 + (1-a)^2 + ... + (1-a)^n).

鉴于此，以及来自 这里，我最终得到了以下实现，这与执行 pandas_dataframe.ewm(span=window_size).mean() 大致等效.

Given this, and with additional spark implementation help from here, I ended up with the following implementation, which is roughly equivalent with doing pandas_dataframe.ewm(span=window_size).mean().

def exponentialMovingAverage(partitionColumn: String, orderColumn: String, column: String, windowSize: Int): DataFrame = {
  val window = Window.partitionBy(partitionColumn)
  val exponentialMovingAveragePrefix = "_EMA_"

  val emaUDF = udf((rowNumber: Int, columnPartitionValues: Seq[Double]) => {
    val alpha = 2.0 / (windowSize + 1)
    val adjustedWeights = (0 until rowNumber + 1).foldLeft(new Array[Double](rowNumber + 1)) { (accumulator, index) =>
      accumulator(index) = pow(1 - alpha, rowNumber - index); accumulator
    }
    (adjustedWeights, columnPartitionValues.slice(0, rowNumber + 1)).zipped.map(_ * _).sum / adjustedWeights.sum
  })
  dataFrame.withColumn("row_nr", row_number().over(window.orderBy(orderColumn)) - lit(1))
    .withColumn(s"$column$exponentialMovingAveragePrefix$windowSize", emaUDF(col("row_nr"), collect_list(column).over(window)))
    .drop("row_nr")
}

(我假设需要计算指数移动平均线的列的类型是 Double.)

(I am presuming the type of the column for which I need to compute the exponential moving average is Double.)

我希望这能帮助其他人.

I hope this helps others.

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