如何从火花数据帧计算滚动协方差矩阵

Question

我有一个Spark 2.2.0 DataFrame的货币价格，我在其中添加了回报。

import org.apache.spark.sql.SparkSession
import org.apache.spark.sql.expressions.Window
import org.apache.spark.sql.functions._

val spark = SparkSession.builder.getOrCreate()
val prices = spark.read.json("prices.json")

// make a window function and convert prices to returns
val window = Window.partitionBy("currency").orderBy("time")
val lagPrice = lag(col("close"), 1).over(window)
val percentReturn = col("close") / col("lastClose") - 1d
val logReturn = log(col("close") / col("lastClose"))

val returns = prices.withColumn("lastClose", lagPrice)
                    .withColumn("return", percentReturn)
                    .withColumn("logReturn", logReturn)

现在我想使用窗口函数计算所有货币的滚动Covarance矩阵（如移动平均线）。但我找不到任何文档或示例。