Calculating a moving average

Calculating a moving average

Problem

You want to calculate a moving average.

Solution

Suppose your data is a noisy sine wave with some missing values:

set.seed(993)
x <- 1:300
y <- sin(x/20) + rnorm(300,sd=.1)
y[251:255] <- NA

The filter() function can be used to calculate a moving average.

## Plot the unsmoothed data (gray)
plot(x, y, type="l", col=grey(.5))
## Draw gridlines
grid()

## Smoothed with lag:
## average of current sample and 19 previous samples (red)
f20 <- rep(1/20, 20)
f20
#>  [1] 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05
#> [18] 0.05 0.05 0.05
y_lag <- filter(y, f20, sides=1)
lines(x, y_lag, col="red")

## Smoothed symmetrically:
## average of current sample, 10 future samples, and 10 past samples (blue)
f21 <- rep(1/21,21)
f21
#>  [1] 0.04761905 0.04761905 0.04761905 0.04761905 0.04761905 0.04761905 0.04761905
#>  [8] 0.04761905 0.04761905 0.04761905 0.04761905 0.04761905 0.04761905 0.04761905
#> [15] 0.04761905 0.04761905 0.04761905 0.04761905 0.04761905 0.04761905 0.04761905
y_sym <- filter(y, f21, sides=2)
lines(x, y_sym, col="blue")

filter() will leave holes wherever it encounters missing values, as shown in the graph above.

A different way to handle missing data is to simply ignore it, and not include it in the average. The function defined here will do that.

## x: the vector
## n: the number of samples
## centered: if FALSE, then average current sample and previous (n-1) samples
##           if TRUE, then average symmetrically in past and future. (If n is even, use one more sample from future.)
movingAverage <- function(x, n=1, centered=FALSE) {

    if (centered) {
        before <- floor  ((n-1)/2)
        after  <- ceiling((n-1)/2)
    } else {
        before <- n-1
        after  <- 0
    }

    # Track the sum and count of number of non-NA items
    s     <- rep(0, length(x))
    count <- rep(0, length(x))

    # Add the centered data
    new <- x
    # Add to count list wherever there isn't a
    count <- count + !is.na(new)
    # Now replace NA_s with 0_s and add to total
    new[is.na(new)] <- 0
    s <- s + new

    # Add the data from before
    i <- 1
    while (i <= before) {
        # This is the vector with offset values to add
        new   <- c(rep(NA, i), x[1:(length(x)-i)])

        count <- count + !is.na(new)
        new[is.na(new)] <- 0
        s <- s + new

        i <- i+1
    }

    # Add the data from after
    i <- 1
    while (i <= after) {
        # This is the vector with offset values to add
        new   <- c(x[(i+1):length(x)], rep(NA, i))

        count <- count + !is.na(new)
        new[is.na(new)] <- 0
        s <- s + new

        i <- i+1
    }

    # return sum divided by count
    s/count
}

## Make same plots from before, with thicker lines
plot(x, y, type="l", col=grey(.5))
grid()
y_lag <- filter(y, rep(1/20, 20), sides=1)
lines(x, y_lag, col="red", lwd=4)         # Lagged average in red
y_sym <- filter(y, rep(1/21,21), sides=2)
lines(x, y_sym, col="blue", lwd=4)        # Symmetrical average in blue

## Calculate lagged moving average with new method and overplot with green
y_lag_na.rm <- movingAverage(y, 20)
lines(x, y_lag_na.rm, col="green", lwd=2)

## Calculate symmetrical moving average  with new method and overplot with green
y_sym_na.rm <- movingAverage(y, 21, TRUE)
lines(x, y_sym_na.rm, col="green", lwd=2)