Vectorized R implementation of exponentially weighted moving average and standard deviation. Outputs the same as Python's default pandas.Series.ewm().

ewm.R

ewma <- function(x, alpha) {
  n <- length(x)
  sapply(
    1:n,
    function(i, x, alpha) {
      y <- x[1:i]
      m <- length(y)
      weights <- (1 - alpha)^((m - 1):0)
      ewma <- sum(weights * y) / sum(weights)
    },
    x = x,
    alpha = alpha
  )
}

ewmsd <- function(x, alpha) {
  n <- length(x)
  sapply(
    1:n,
    function(i, x, alpha) {
      y <- x[1:i]
      m <- length(y)
      weights <- (1 - alpha)^((m - 1):0)
      ewma <- sum(weights * y) / sum(weights)
      bias <- sum(weights)^2 / (sum(weights)^2 - sum(weights^2))
      ewmsd <- sqrt(bias * sum(weights * (y - ewma)^2) / sum(weights))
    },
    x = x,
    alpha = alpha
  )
}

https://stackoverflow.com/questions/54585015/vectorized-implementation-of-exponentially-weighted-moving-standard-deviation-us