ema: Exponential Moving Average

In AkselA/R-rollfun:

Description

ema returns a vector whose values are the exponentially smoothed values of the input vector

Usage

ema(x, a = 2, burnin = 1)

Arguments

x	numeric; input vector
a	numeric; smoothing factor
burnin	integer or "auto"; set the initial estimate (S[1]) to the average of the first N values of X S[1] = mean(X[1:N]) Default is 1, if "auto" is selected it will be set to ceiling(a).

Details

With X[t] being the input at time t, S[t] being the output at time t, and α = 1/a
– the default function can be defined like this:

S[t] = {X[1] for t = 1; α * X[t] + (1 - α) * S[t-1] for t > 1}

The function is also sometimes referred to as an exponentially weighted moving average (EWMA).

See Also

dema, iema

Examples

x <- c(rep(0, 4), 1, rep(0, 59))
a <- 1:10*5
col <- rainbow(length(a), start=0.15)

plot(x, type="p", pch=16, cex=0.4, ylim=c(0, 0.21), xaxs="i",
  main="Exponential Moving Average", xlab="Time", ylab="Magnitude")
for (i in seq_along(a)) {
    lines(ema(x, a[i]), col=col[i])
}

mtext("Single impulse of magnitude 1 occuring at time = 5", line=0.2)
L <- lapply(seq_along(a), function(x) bquote(alpha ==  1 / .(a[x])))
legend("topright", legend=as.expression(L),
  bty="n", col=col, lwd=1.2, cex=0.8, y.intersp=1.2)

# Works well with missing data
# Burnin can be useful to quickly stabalize the filter
set.seed(4)
re <- rexp(50) * sqrt(50:1)
re[sample(1:50, 5)] <- NA

plot(re)
lines(ema(re, 9, burnin=1), col="red")
lines(ema(re, 9, burnin=5), col="blue")
lines(ema(re, 9, burnin="auto"), col="green")

AkselA/R-rollfun documentation built on May 31, 2019, 8:41 a.m.