Computing EWMA

As a loop oriented developer—and long time user of old static typed languages—my first attempt to compute EWMA in R was

ewma.loop <- function(rets, lambda) {
    n <- length(rets)+1
    sig.s <- rep(0, n)
    for (i in 2:n) {
        sig.s[i] <- sig.s[i-1]*lambda + (rets[i-1]^2)*(1 - lambda)
    }
    return(sqrt(tail(sig.s, n-1)))
}

At a first sigh this implementation seemed to be good but from the perspective of an R developer it isn't. Avoiding loops would be a better. After a little research I found

ewma.func <- function(rets, lambda) {
    sig.p <- 0
    sig.s <- vapply(rets, function(r) sig.p <<- sig.p*lambda + (r^2)*(1 - lambda), 0)
    return(sqrt(sig.s))
}

This implementation looked clean and sexy to me and it also reveals the power of *apply functions. I decided to evaluate the performance of both implementations in order to find out which one is really the best.

lambda <- 0.94
rets <- 0.02*rnorm(100)
system.time( replicate(10000, ewma.loop(rets, lambda)) )
# user  system elapsed 
# 4.075   0.018   4.093 
system.time( replicate(10000, ewma.func(rets, lambda)) )
# user  system elapsed 
# 2.271   0.001   2.272

The results are amazing. Using functional approach is, without doubt, much better. It is almost 2 times better and this is significant.