```
# show effect of pad
running(1:20, width = 5)
running(1:20, width = 5, pad = TRUE)
# show effect of align
running(1:20, width = 5, align = "left", pad = TRUE)
running(1:20, width = 5, align = "center", pad = TRUE)
running(1:20, width = 5, align = "right", pad = TRUE)
# show effect of simplify
running(1:20, width = 5, fun = function(x) x) # matrix
running(1:20, width = 5, fun = function(x) x, simplify = FALSE) # list
# show effect of by
running(1:20, width = 5) # normal
running(1:20, width = 5, by = 5) # non-overlapping
running(1:20, width = 5, by = 2) # starting every 2nd
# Use 'pad' to ensure correct length of vector, also show the effect
# of allow.fewer.
par(mfrow = c(2, 1))
plot(1:20, running(1:20, width = 5, allow.fewer = FALSE, pad = TRUE), type = "b")
plot(1:20, running(1:20, width = 5, allow.fewer = TRUE, pad = TRUE), type = "b")
par(mfrow = c(1, 1))
# plot running mean and central 2 standard deviation range
# estimated by *last* 40 observations
dat <- rnorm(500, sd = 1 + (1:500) / 500)
plot(dat)
sdfun <- function(x, sign = 1) mean(x) + sign * sqrt(var(x))
lines(running(dat, width = 51, pad = TRUE, fun = mean), col = "blue")
lines(running(dat, width = 51, pad = TRUE, fun = sdfun, sign = -1), col = "red")
lines(running(dat, width = 51, pad = TRUE, fun = sdfun, sign = 1), col = "red")
# plot running correlation estimated by last 40 observations (red)
# against the true local correlation (blue)
sd.Y <- seq(0, 1, length = 500)
X <- rnorm(500, sd = 1)
Y <- rnorm(500, sd = sd.Y)
plot(running(X, X + Y, width = 20, fun = cor, pad = TRUE), col = "red", type = "s")
r <- 1 / sqrt(1 + sd.Y^2) # true cor of (X,X+Y)
lines(r, type = "l", col = "blue")
```

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