CODEWITHSUNDEEP
scalaapache-sparkapache-spark-sql
cristi.calugaru
cristi.calugaru

Reputation: 601

Spark Exponential Moving Average

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

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

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)

where 

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

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"))

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

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.

Any ideas?

Upvotes: 4

Views: 5375

Answers (1)

cristi.calugaru
cristi.calugaru

Reputation: 601

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).

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")
}

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

I hope this helps others.

Upvotes: 8

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