# rollapply

##### Apply Rolling Functions

A generic function for applying a function to rolling margins of an array.

##### Usage

```
rollapply(data, ...)
## S3 method for class 'ts':
rollapply(data, \dots)
## S3 method for class 'zoo':
rollapply(data, width, FUN, \dots, by = 1, by.column = TRUE,
fill = if (na.pad) NA, na.pad = FALSE, partial = FALSE,
align = c("center", "left", "right"))
## S3 method for class 'default':
rollapply(data, \dots)
rollapplyr(..., align = "right")
```

##### Arguments

- data
- the data to be used (representing a series of observations).
- width
- numeric vector or list. In the simplest case this is an integer
specifying the window width which is aligned to the original sample according
to the
`align`

argument. Alternatively,`width`

can be a list regarded as offse - FUN
- the function to be applied.
- ...
- optional arguments to
`FUN`

. - by
- calculate FUN at every
`by`

-th time point rather than every point.`by`

is only used if`width`

is length 1 and either a plain scalar or a list. - by.column
- logical. If
`TRUE`

,`FUN`

is applied to each column separately. - fill
- a three-component vector or list (recycled otherwise) providing
filling values at the left/within/to the right of the data range.
See the
`fill`

argument of`na.fill`

for details. - na.pad
- deprecated. Use
`fill = NA`

instead of`na.pad = TRUE`

. - partial
- logical or numeric. If
`FALSE`

(default) then`FUN`

is only applied when all indexes of the rolling window are within the observed time range. If`TRUE`

, then the subset of indexes that are in range are passed to - align
- specifyies whether the index of the result
should be left- or right-aligned or centered (default) compared
to the rolling window of observations. This argument is only used if
`width`

represents widths.

##### Details

If `width`

is a plain numeric vector its elements are regarded as widths
to be interpreted in conjunction with `align`

whereas if `width`

is a list
its components are regarded as offsets. In the above cases if the length of
`width`

is 1 then `width`

is recycled for every `by`

-th point.
If `width`

is a list its components represent integer offsets such that
the i-th component of the list refers to time points at positions
`i + width[[i]]`

. If any of these points are below 1 or above the
length of `index(data)`

then `FUN`

is not evaluated for that
point unless `partial = TRUE`

and in that case only the valid
points are passed.

The rolling function can also be applied to partial windows by setting `partial = TRUE`

For example, if `width = 3, align = "right"`

then for the first point
just that point is passed to `FUN`

since the two points to its
left are out of range. For the same example, if `partial = FALSE`

then `FUN`

is not
invoked at all for the first two points. If `partial`

is a numeric then it
specifies the minimum number of offsets that must be within range. Negative
`partial`

is interpreted as `FALSE`

.

If `FUN`

is `mean`

, `max`

or `median`

and `by.column`

is
`TRUE`

and width is a plain scalar and there are no other arguments
then special purpose code is used to enhance performance.
Also in the case of `mean`

such special purpose code is only invoked if the
`data`

argument has no `NA`

values.
See `rollmean`

, `rollmax`

and `rollmedian`

for more details.
Currently, there are methods for `"zoo"`

and `"ts"`

series
and `"default"`

method for ordinary vectors and matrices.

`rollapplyr`

is a wrapper around `rollapply`

that uses a default
of `align = "right"`

.

##### Value

- A object of the same class as
`data`

with the results of the rolling function.

##### See Also

##### Examples

```
## rolling mean
z <- zoo(11:15, as.Date(31:35))
rollapply(z, 2, mean)
## non-overlapping means
z2 <- zoo(rnorm(6))
rollapply(z2, 3, mean, by = 3) # means of nonoverlapping groups of 3
aggregate(z2, c(3,3,3,6,6,6), mean) # same
## optimized vs. customized versions
rollapply(z2, 3, mean) # uses rollmean which is optimized for mean
rollmean(z2, 3) # same
rollapply(z2, 3, (mean)) # does not use rollmean
## rolling regression:
## set up multivariate zoo series with
## number of UK driver deaths and lags 1 and 12
seat <- as.zoo(log(UKDriverDeaths))
time(seat) <- as.yearmon(time(seat))
seat <- merge(y = seat, y1 = lag(seat, k = -1),
y12 = lag(seat, k = -12), all = FALSE)
## run a rolling regression with a 3-year time window
## (similar to a SARIMA(1,0,0)(1,0,0)_12 fitted by OLS)
rr <- rollapply(seat, width = 36,
FUN = function(z) coef(lm(y ~ y1 + y12, data = as.data.frame(z))),
by.column = FALSE, align = "right")
## plot the changes in coefficients
## showing the shifts after the oil crisis in Oct 1973
## and after the seatbelt legislation change in Jan 1983
plot(rr)
## different values of rule argument
z <- zoo(c(NA, NA, 2, 3, 4, 5, NA))
rollapply(z, 3, sum, na.rm = TRUE)
rollapply(z, 3, sum, na.rm = TRUE, fill = NULL)
rollapply(z, 3, sum, na.rm = TRUE, fill = NA)
rollapply(z, 3, sum, na.rm = TRUE, partial = TRUE)
# this will exclude time points 1 and 2
# It corresonds to align = "right", width = 3
rollapply(zoo(1:8), list(seq(-2, 0)), sum)
# but this will include points 1 and 2
rollapply(zoo(1:8), list(seq(-2, 0)), sum, partial = 1)
rollapply(zoo(1:8), list(seq(-2, 0)), sum, partial = 0)
# so will this
rollapply(zoo(1:8), list(seq(-2, 0)), sum, fill = NA)
# by = 3, align = "right"
L <- rep(list(NULL), 8)
L[seq(3, 8, 3)] <- list(seq(-2, 0))
str(L)
rollapply(zoo(1:8), L, sum)
rollapply(zoo(1:8), list(0:2), sum, fill = 1:3)
rollapply(zoo(1:8), list(0:2), sum, fill = 3)
L2 <- rep(list(-(2:0)), 10)
L2[5] <- list(NULL)
str(L2)
rollapply(zoo(1:10), L2, sum, fill = "extend")
rollapply(zoo(1:10), L2, sum, fill = list("extend", NULL))
rollapply(zoo(1:10), L2, sum, fill = list("extend", NA))
rollapply(zoo(1:10), L2, sum, fill = NA)
rollapply(zoo(1:10), L2, sum, fill = 1:3)
rollapply(zoo(1:10), L2, sum, partial = TRUE)
rollapply(zoo(1:10), L2, sum, partial = TRUE, fill = 99)
rollapply(zoo(1:10), list(-1), sum, partial = 0)
rollapply(zoo(1:10), list(-1), sum, partial = TRUE)
rollapply(zoo(cbind(a = 1:6, b = 11:16)), 3, rowSums, by.column = FALSE)
# these two are the same
rollapply(zoo(cbind(a = 1:6, b = 11:16)), 3, sum)
rollapply(zoo(cbind(a = 1:6, b = 11:16)), 3, colSums, by.column = FALSE)
# these two are the same
rollapply(zoo(1:6), 2, sum, by = 2, align = "right")
aggregate(zoo(1:6), c(2, 2, 4, 4, 6, 6), sum)
# these two are the same
rollapply(zoo(1:3), list(-1), c)
lag(zoo(1:3), -1)
# these two are the same
rollapply(zoo(1:3), list(1), c)
lag(zoo(1:3))
# these two are the same
rollapply(zoo(1:5), list(c(-1, 0, 1)), sum)
rollapply(zoo(1:5), 3, sum)
# these two are the same
rollapply(zoo(1:5), list(0:2), sum)
rollapply(zoo(1:5), 3, sum, align = "left")
# these two are the same
rollapply(zoo(1:5), list(-(2:0)), sum)
rollapply(zoo(1:5), 3, sum, align = "right")
# these two are the same
rollapply(zoo(1:6), list(NULL, NULL, -(2:0)), sum)
rollapply(zoo(1:6), 3, sum, by = 3, align = "right")
# these two are the same
rollapply(zoo(1:5), list(c(-1, 1)), sum)
rollapply(zoo(1:5), 3, function(x) sum(x[-2]))
# these two are the same
rollapply(1:5, 3, rev)
embed(1:5, 3)
# these four are the same
x <- 1:6
rollapply(c(0, 0, x), 3, sum, align = "right") - x
rollapply(x, 3, sum, partial = TRUE, align = "right") - x
rollapply(x, 3, function(x) sum(x[-3]), partial = TRUE, align = "right")
rollapply(x, list(-(2:1)), sum, partial = 0)
# same as Matlab's buffer(x, n, p) for valid non-negative p
# See http://www.mathworks.com/help/toolbox/signal/buffer.html
x <- 1:30; n <- 7; p <- 3
t(rollapply(c(rep(0, p), x, rep(0, n-p)), n, by = n-p, c))
# these three are the same
y <- 10 * seq(8); k <- 4; d <- 2
# 1
# from http://ucfagls.wordpress.com/2011/06/14/embedding-a-time-series-with-time-delay-in-r-part-ii/
Embed <- function(x, m, d = 1, indices = FALSE, as.embed = TRUE) {
n <- length(x) - (m-1)*d
X <- seq_along(x)
if(n <= 0)
stop("Insufficient observations for the requested embedding")
out <- matrix(rep(X[seq_len(n)], m), ncol = m)
out[,-1] <- out[,-1, drop = FALSE] +
rep(seq_len(m - 1) * d, each = nrow(out))
if(as.embed)
out <- out[, rev(seq_len(ncol(out)))]
if(!indices)
out <- matrix(x[out], ncol = m)
out
}
Embed(y, k, d)
# 2
rollapply(y, list(-d * seq(0, k-1)), c)
# 3
rollapply(y, d*k-1, function(x) x[d * seq(k-1, 0) + 1])
```

*Documentation reproduced from package zoo, version 1.7-6, License: GPL-2*