Smoothing: What is it good for?

Let’s say we have a crazy noisy time series where we have perhaps oversampled and encounter spurious variability. Smoothing to the rescue

Let’s generate and plot some noisy data

1000 observations sampled from a random normal distrubution. mean=20, var=10

test <- data.frame(noisydat = rnorm(1000, 20, 2))
# for plotting, we need a sequence variable
dat <- test %>%
    mutate(myseq = seq_along(noisydat))
head(dat, n = 15)
noisydat myseq
20.68 1
17.46 2
21.72 3
19.12 4
17.90 5
17.04 6
18.80 7
21.08 8
20.03 9
20.91 10
22.13 11
18.19 12
16.79 13
18.81 14
17.70 15 
ggplot(dat, aes(x = myseq, y = noisydat)) + geom_line(color = "red", alpha = 0.7) +
    ylim(c(15, 25)) + jamie.theme

#Rolling mean on the noisy mydat vector This comoputes a simple noving average for the window size (k) you specify. That is, every n’th observation is averaged with the k past observations to derive a rolling mean for that replaces the original observation reducing its unique variability.

smoothed <- dat %>%
    mutate(smoothdat = zoo::rollmean(noisydat, k = 5, fill = NA))  #use a moving window of 5
head(smoothed, n = 15)
noisydat myseq smoothdat
20.68 1 NA
17.46 2 NA
21.72 3 19.38
19.12 4 18.65
17.90 5 18.92
17.04 6 18.79
18.80 7 18.97
21.08 8 19.57
20.03 9 20.59
20.91 10 20.47
22.13 11 19.61
18.19 12 19.37
16.79 13 18.73
18.81 14 18.77
17.70 15 18.23 
ggplot(smoothed, aes(x = myseq, y = smoothdat)) + geom_line(color = "goldenrod2",
    alpha = 0.7) + ylim(c(15, 25)) + jamie.theme