Create rolling windows with custom overlap

Question

I'd like to analyse time-series data along multiple rolling windows. As a first step, I'd like to extract the start and end-times of said windows. Sadly, using zoo:rollapply seems to be missing a crucial parameter, namely the overlap, which seems to fixed at 1?

Example:

library(zoo)
a <- c(0:10)
output <- rollapply(a, 4, print)

output:

      [,1] [,2] [,3] [,4]
[1,]    0    1    2    3
[2,]    1    2    3    4
[3,]    2    3    4    5
[4,]    3    4    5    6
[5,]    4    5    6    7
[6,]    5    6    7    8
[7,]    6    7    8    9
[8,]    7    8    9   10

desired output (having an overlap of 2, for example):

     [,1] [,2] [,3] [,4]
[1,]    0    1    2    3
[2,]    2    3    4    5
[3,]    4    5    6    7
[4,]    6    7    8    9
[5,]    8    9    10

any idea of how to get there?

by = 2 sounds very good! Thanks! I did overlook it... I'll try later — Beres
– Beres, Commented Mar 12 at 15:17

Gwang-Jin Kim · Accepted Answer · 2025-03-13 15:33:35Z

3

A combination of by=2 for 2 steps per row and adding some NA's at the end makes it:

> rollapply(c(v, NA, NA), width=4, FUN=`c`, by=2)
     [,1] [,2] [,3] [,4]
[1,]    0    1    2    3
[2,]    2    3    4    5
[3,]    4    5    6    7
[4,]    6    7    8    9
[5,]    8    9   10   NA

(Given that v <- 0:10 ).

I thought fill=NA would make it, but it does not.

c(v, NA, NA) the number of NA should be the number of by, eventually.

If so, use the function:

fill_up <- function(vec, by, default=NA) c(vec, rep(default, by))

rolling_window <- function(vec, width, by, FUN=`c`, default=NA) {
  rollapply(fill_up(vec, by, default=default), width=width, by=by, FUN=FUN)
}

And call it by:

rolling_window(vec=v, width=4, by=2)

Value-Window

If you want to have instead of the width a value window, then the output will be a list of vectors (because not any more a constant number of elements in one group/"row".

I would write a new for that.

require(zoo)

v <- c(100, 200, 300, 500, 600, 900, 1000, 1200, 1300, 1500)

rolling_absolute_window <- function(vec, window_width=300) {
  start_value <- vec[[1]]
  end_value <- vec[[length(vec)]]
  limits <- seq(from=start_value, to=end_value, by=window_width)
  limits_df <- rollapply(c(limits, Inf), width=2, FUN=`c`, by=1)
  lapply(as.data.frame(t(limits_df)), function(pair) {
    vec[pair[1] <= vec & vec <= pair[2]]
  })
}

rolling_absolute_window(v)

## this would return:

$V1
[1] 100 200 300

$V2
[1] 500 600

$V3
[1]  900 1000

$V4
[1] 1000 1200 1300

$V5
[1] 1300 1500

rolling_absolute_window_excluding_last <- function(vec, window_width=300) {
  start_value <- vec[[1]]
  end_value <- vec[[length(vec)]]
  limits <- seq(from=start_value, to=end_value, by=window_width)
  limits_df <- rollapply(c(limits, Inf), width=2, FUN=`c`, by=1)
  lapply(as.data.frame(t(limits_df)), function(pair) {
    vec[pair[1] <= vec & vec < pair[2]]   # excludes last
  })
}

rolling_absolute_window_excluding_last(v)

## this returns:

$V1
[1] 100 200 300

$V2
[1] 500 600

$V3
[1] 900

$V4
[1] 1000 1200

$V5
[1] 1300 1500


rolling_window <- function(vec, window_width=300) {
  result <- list()
  for (i in 1:length(vec)) {
    result[[i]] <- vec[ vec[i] <= vec & vec <= vec[i] + window_width]
  }
  result[-length(vec)]
}

rolling_window(v)

## this would return:

[[1]]
[1] 100 200 300

[[2]]
[1] 200 300 500

[[3]]
[1] 300 500 600

[[4]]
[1] 500 600

[[5]]
[1] 600 900

[[6]]
[1]  900 1000 1200

[[7]]
[1] 1000 1200 1300

[[8]]
[1] 1200 1300 1500

[[9]]
[1] 1300 1500



rolling_window_excluding_last <- function(vec, window_width=300) {
  result <- list()
  for (i in 1:length(vec)) {
    result[[i]] <- vec[ vec[i] <= vec & vec < vec[i] + window_width]
  }
  result[-length(vec)]
}

rolling_window_excluding_last(v)

## which returns:

[[1]]
[1] 100 200 300

[[2]]
[1] 200 300

[[3]]
[1] 300 500

[[4]]
[1] 500 600

[[5]]
[1] 600

[[6]]
[1]  900 1000

[[7]]
[1] 1000 1200

[[8]]
[1] 1200 1300

[[9]]
[1] 1300 1500

edited Mar 13 at 15:33

answered Mar 12 at 15:18

Gwang-Jin Kim

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10 Comments

Beres Mar 12 at 15:23

is it generalizable? I'm confused by v, NA, NA

Gwang-Jin Kim Mar 12 at 15:24

I guess number of NA shoul dbe the number of by?

Beres Mar 12 at 21:14

works great! But I am wondering, what if the values in the vector that I am cutting rolling windows from mean something? To clarify: let's say a <- c(100, 200, 300, 500, 600, 900, 1000, 1200, 1300, 1500) and I'd like to make the rolling window 300 wide, i.e. widthwould not be steps in the vector, but a fixed distance between values, that the result would be (100, 200, 300), (200,500), (500, 600), (600,900), (900, 1200)

Gwang-Jin Kim Mar 13 at 9:08

In that case, you can't use rollapply - it is only for even widths. You need a recursive function then which executes step by step.

G. Grothendieck Mar 13 at 13:11

@Beres, You need to define more precisely what 300 wide means but if we assume that for each i = 1, 2, 3, ... we want the x values that satisfy a[i]-300 <= x <= a[i] then w <- seq_along(a) - findInterval(a - 300, a); rollapplyr(a, w, toString) . There are examples of this in ?rollapply

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