# Volume-weighted Exponential Moving Average

September 27, 2013
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While I was working on a smoothing function, I came across the EMA (exponential moving average) which basically applies exponentially-decreasing weights to older observations. This is commonly used in finance, and can offer some protection against lags in trend movements.

As I was looking to combine this moving average with a volume-weighted version, or simply a weighted moving average, I ran across this Volume-weighted Exponential Moving Average stuff from Peter Ponzo. I gave it a try in R and here’s the code.

 ```1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 ``` ```VEMA <- function(x, volumes, n = 10, wilder = F, ratio = NULL, ...) { x <- try.xts(x, error = as.matrix) if (n < 1 || n > NROW(x)) stop("Invalid 'n'") if (any(nNonNA <- n > colSums(!is.na(x)))) stop("n > number of non-NA values in column(s) ", paste(which(nNonNA), collapse = ", ")) x.na <- xts:::naCheck(x, n) if (missing(n) && !missing(ratio)) n <- trunc(2/ratio - 1) if (is.null(ratio)) { if (wilder) ratio <- 1/n else ratio <- 2/(n + 1) }   foo <- cbind(x[,1], volumes, VEMA.num(as.numeric(x[,1]), volumes, ratio), VEMA.den(volumes, ratio)) (foo[,3] / foo[,4]) -> ma   ma <- reclass(ma, x) if (!is.null(dim(ma))) { colnames(ma) <- paste(colnames(x), "VEMA", n, sep = ".") } return(ma) }   VEMA.num <- function(x, volumes, ratio) { ret <- c() s <- 0 for(i in 1:length(x)) { s <- ratio * s + (1-ratio) * x[i] * volumes[i]; ret <- c(ret, s); } ret }   VEMA.den <- function(volumes, ratio) { ret <- c() s <- 0 for(i in 1:length(x)) { s <- ratio * s + (1-ratio) * volumes[i]; ret <- c(ret, s); } ret }   VEMA(1:20, 20:1, ratio=0.1)   VEMA(1:20, 20:1, ratio=0.9)```

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