Calculating moving average

Question

I'm trying to use R to calculate the moving average over a series of values in a matrix. The normal R mailing list search hasn't been very helpful though. There doesn't seem to be a built-in function in R will allow me to calculate moving averages. Do any packages provide one? Or do I need to write my own?

Answer 1

• Rolling Means/Maximums/Medians in the zoo package (rollmean)
• MovingAverages in TTR
• ma in forecast

Answer 2

Or you can simply calculate it using filter, here's the function I use:

ma <- function(x, n = 5){filter(x, rep(1 / n, n), sides = 2)}

If you use dplyr, be careful to specify stats::filter in the function above.

Answer 3

Using cumsum should be sufficient and efficient. Assuming you have a vector x and you want a running sum of n numbers

cx <- c(0,cumsum(x))
rsum <- (cx[(n+1):length(cx)] - cx[1:(length(cx) - n)]) / n

As pointed out in the comments by @mzuther, this assumes that there are no NAs in the data. to deal with those would require dividing each window by the number of non-NA values. Here's one way of doing that, incorporating the comment from @Ricardo Cruz:

cx <- c(0, cumsum(ifelse(is.na(x), 0, x)))
cn <- c(0, cumsum(ifelse(is.na(x), 0, 1)))
rx <- cx[(n+1):length(cx)] - cx[1:(length(cx) - n)]
rn <- cn[(n+1):length(cx)] - cn[1:(length(cx) - n)]
rsum <- rx / rn

This still has the issue that if all the values in the window are NAs then there will be a division by zero error.

Answer 4

In data.table 1.12.0 new frollmean function has been added to compute fast and exact rolling mean carefully handling NA, NaN and +Inf, -Inf values.

As there is no reproducible example in the question there is not much more to address here.

You can find more info about ?frollmean in manual, also available online at ?frollmean.

Examples from manual below:

library(data.table)
d = as.data.table(list(1:6/2, 3:8/4))

# rollmean of single vector and single window
frollmean(d[, V1], 3)

# multiple columns at once
frollmean(d, 3)

# multiple windows at once
frollmean(d[, .(V1)], c(3, 4))

# multiple columns and multiple windows at once
frollmean(d, c(3, 4))

## three above are embarrassingly parallel using openmp

Answer 5

The caTools package has very fast rolling mean/min/max/sd and few other functions. I've only worked with runmean and runsd and they are the fastest of any of the other packages mentioned to date.

Answer 6

You could use RcppRoll for very quick moving averages written in C++. Just call the roll_mean function. Docs can be found here.

Otherwise, this (slower) for loop should do the trick:

ma <- function(arr, n=15){
  res = arr
  for(i in n:length(arr)){
    res[i] = mean(arr[(i-n):i])
  }
  res
}

Answer 7

In fact RcppRoll is very good.

The code posted by cantdutchthis must be corrected in the fourth line to the window be fixed:

ma <- function(arr, n=15){
  res = arr
  for(i in n:length(arr)){
    res[i] = mean(arr[(i-n+1):i])
  }
  res
}

Another way, which handles missings, is given here.

A third way, improving cantdutchthis code to calculate partial averages or not, follows:

  ma <- function(x, n=2,parcial=TRUE){
  res = x #set the first values

  if (parcial==TRUE){
    for(i in 1:length(x)){
      t<-max(i-n+1,1)
      res[i] = mean(x[t:i])
    }
    res

  }else{
    for(i in 1:length(x)){
      t<-max(i-n+1,1)
      res[i] = mean(x[t:i])
    }
    res[-c(seq(1,n-1,1))] #remove the n-1 first,i.e., res[c(-3,-4,...)]
  }
}

Answer 8

In order to complement the answer of cantdutchthis and Rodrigo Remedio;

moving_fun <- function(x, w, FUN, ...) {
  # x: a double vector
  # w: the length of the window, i.e., the section of the vector selected to apply FUN
  # FUN: a function that takes a vector and return a summarize value, e.g., mean, sum, etc.
  # Given a double type vector apply a FUN over a moving window from left to the right, 
  #    when a window boundary is not a legal section, i.e. lower_bound and i (upper bound) 
  #    are not contained in the length of the vector, return a NA_real_
  if (w < 1) {
    stop("The length of the window 'w' must be greater than 0")
  }
  output <- x
  for (i in 1:length(x)) {
     # plus 1 because the index is inclusive with the upper_bound 'i'
    lower_bound <- i - w + 1
    if (lower_bound < 1) {
      output[i] <- NA_real_
    } else {
      output[i] <- FUN(x[lower_bound:i, ...])
    }
  }
  output
}

# example
v <- seq(1:10)

# compute a MA(2)
moving_fun(v, 2, mean)

# compute moving sum of two periods
moving_fun(v, 2, sum)

Answer 9

Though a bit slow but you can also use zoo::rollapply to perform calculations on matrices.

reqd_ma <- rollapply(x, FUN = mean, width = n)

where x is the data set, FUN = mean is the function; you can also change it to min, max, sd etc and width is the rolling window.