# Apply any R function on rolling windows

#### Dawid Kałędkowski

#### 2025-11-30

## Using runner

`runner` package provides functions applied on running windows. The most universal function is `runner::runner` which gives user possibility to apply any R function `f` on running windows. Running windows are defined for each data window size `k`, `lag` with respect to their indexes. Unlike other available R packages, `runner` supports any input and output type and also gives full control to manipulate window size and lag/lead.

There are different kinds of running windows and all of them are implemented in `runner`.

### Cumulative windows

The simplest window type which is similar to `base::cumsum`. At each element window is defined by all elements appearing before current.

In `runner` this can be achieved as simple by:

    library(runner)
    # full windows
    runner(1:15)

    # summarizing - sum
    runner(
      1:15,
      f = sum
    )

    # summarizing - concatenating
    runner(
      letters[1:15],
      f = paste,
      collapse = " > "
    )

### Constant sliding windows

Second type of windows are these commonly known as running/rolling/moving/sliding windows. This types of windows moves along the index instead of cumulating like a previous one.
Following diagram illustrates running windows of length `k = 4`. Each of 15 windows contains 4 elements (except first three).

To obtain constant sliding windows one just needs to specify `k` argument

    # summarizing - sum of 4-elements
    runner(
      1:15,
      k = 4,
      f = sum
    )

    # summarizing - slope from lm
    df <- data.frame(
      a = 1:15,
      b = 3 * 1:15 + rnorm(15)
    )

    runner(
      x = df,
      k = 5,
      f = function(x) {
        model <- lm(b ~ a, data = x)
        coefficients(model)["a"]
      }
    )

### Windows depending on date

By default `runner` calculates on assumption that index increments by one, but sometimes data points in dataset are not equally spaced (missing weekends, holidays, other missings) and thus window size should vary to keep expected time frame. If one specifies `idx` argument, than running functions are applied on windows depending on date rather on a sequence 1-n. `idx` should be the same length as `x` and should be of type `Date`, `POSIXt` or `integer`. Example below illustrates window of size `k = 5` lagged by `lag = 1`. Note that one can specify also `k = "5 days"` and `lag = "day"` as in `seq.POSIXt`.
In the example below in square brackets ranges for each window.

    idx <- c(4, 6, 7, 13, 17, 18, 18, 21, 27, 31, 37, 42, 44, 47, 48)

    # summarize - mean
    runner::runner(
      x = idx,
      k = 5, # 5-days window
      lag = 1,
      idx = idx,
      f = function(x) mean(x)
    )

    # use Date or datetime sequences
    runner::runner(
      x = idx,
      k = "5 days", # 5-days window
      lag = 1,
      idx = Sys.Date() + idx,
      f = function(x) mean(x)
    )

    # obtain window from above illustration
    runner::runner(
      x = idx,
      k = "5 days",
      lag = 1,
      idx = Sys.Date() + idx
    )

### running at

Runner by default returns vector of the same size as `x` unless one puts any-size vector to `at` argument. Each element of `at` is an index on which runner calculates function. Example below illustrates output of runner for `at = c(13, 27, 45, 31)` which gives windows in ranges enclosed in square brackets. Range for `at = 27` is `[22, 26]` which is not available in current indices.

    idx <- c(4, 6, 7, 13, 17, 18, 18, 21, 27, 31, 37, 42, 44, 47, 48)

    # summary
    runner::runner(
      x = 1:15,
      k = 5,
      lag = 1,
      idx = idx,
      at = c(18, 27, 48, 31),
      f = mean
    )

    # full window
    runner::runner(
      x = idx,
      k = 5,
      lag = 1,
      idx = idx,
      at = c(18, 27, 48, 31)
    )

`at` can also be specified as interval of the output defined by time interval which results in obtaining results on following indices `seq(min(idx), max(idx), by = "<time interval>")`. Interval can be set in the same way as in `seq.POSIXt` function. It’s worth noting that `at` interval shouldn’t be more frequent than interval of `idx` - for `Date` the most frequent interval is a `"day"`, for `POSIXt` it’s a `"sec"`.

    idx_date <- seq(Sys.Date(), Sys.Date() + 365, by = "1 month")

    # change interval to 4-months
    runner(
      x = 0:12,
      idx = idx_date,
      at = "4 months"
    )

    # calculate correlation at every 6-months
    runner(
      x = data.frame(
        a = 1:13,
        b = 1:13 + rnorm(13, sd = 5),
        idx_date
      ),
      idx = "idx_date",
      at = "6 months",
      f = function(x) {
        cor(x$a, x$b)
      }
    )

### Move and stretch window in time

One can stretch window length by `k` and shift in time (or index) using `lag`. Both arguments can be `integer` and also time interval like for example `2 months`. If `k` or `lag` are a single value then window size/lag are constant for all elements of x. User can also specify `k/lag` as vector, then size and lag will vary for each window. Both `k` and `lag` can be of `length(.) == 1`, `length(.) == length(x)` or `length(.) == length(at)` (if `at` is specified). `lag` can be negative and positive while `k` only non-negative.

    # summarizing - concatenating
    runner::runner(
      x = 1:10,
      lag = c(-1, 2, -1, -2, 0, 0, 5, -5, -2, -3),
      k = c(0, 1, 1, 1, 1, 5, 5, 5, 5, 5),
      f = paste,
      collapse = ","
    )

    # full window
    runner::runner(
      x = 1:10,
      lag = 1,
      k = c(1, 1, 1, 1, 1, 5, 5, 5, 5, 5)
    )

    # on dates
    idx <- c(4, 6, 7, 13, 17, 18, 18, 21, 27, 31, 37, 42, 44, 47, 48)

    runner::runner(
      x = 1:15,
      lag = sample(c("-2 days", "-1 days", "1 days", "2 days"),
        size = 15,
        replace = TRUE
      ),
      k = sample(c("5 days", "10 days", "15 days"),
        size = 15,
        replace = TRUE
      ),
      idx = Sys.Date() + idx,
      f = function(x) mean(x)
    )

### `NA` padding

Using `runner` one can also specify `na_pad = TRUE` which would return `NA` for any window which is partially out of range - meaning that there is no sufficient number of observations to fill the window. By default `na_pad = FALSE`, which means that incomplete windows are calculated anyway. `na_pad` is applied on normal cumulative windows and on windows depending on date. In example below two windows exceed range given by `idx` so for these windows are empty for `na_pad = TRUE`. If used sets `na_pad = FALSE` first window will be empty (no single element within `[-2, 3]`) and last window will return elements within matching `idx`.

    idx <- c(4, 6, 7, 13, 17, 18, 18, 21, 27, 31, 37, 42, 44, 47, 48)

    runner::runner(
      x = 1:15,
      k = 5,
      lag = 1,
      idx = idx,
      at = c(4, 18, 48, 51),
      na_pad = TRUE,
      f = function(x) mean(x)
    )

### Using runner with `data.frame`

User can also put `data.frame` into `x` argument and apply functions which involve multiple columns. In example below we calculate beta parameter of `lm` model on 1, 2, …, n observations respectively. On the plot one can observe how `lm` parameter adapt with increasing number of observation.

    x <- cumsum(rnorm(40))
    y <- 3 * x + rnorm(40)
    date <- Sys.Date() + cumsum(sample(1:3, 40, replace = TRUE)) # unequaly spaced time series
    group <- rep(c("a", "b"), 20)

    df <- data.frame(date, group, y, x)

    slope <- runner(
      df,
      function(x) {
        coefficients(lm(y ~ x, data = x))[2]
      }
    )

    plot(slope)

One can also use `runner` with `dplyr` also with problematic `group_by` operations, without need to apply group_modify. Below we apply grouped 20-days beta, by specifying window length `k = "10 days"` and providing column name where indices (dates) are kept.

    library(dplyr)

    summ <- df %>%
      group_by(group) %>%
      mutate(
        cumulative_mse = runner(
          x = .,
          k = "20 days",
          idx = "date", # specify column name instead df$date
          f = function(x) {
            coefficients(lm(y ~ x, data = x))[2]
          }
        )
      )

    library(ggplot2)
    summ %>%
      ggplot(aes(x = date, y = cumulative_mse, group = group, color = group)) +
      geom_line()

When user executes multiple `runner` calls in `dplyr` mutate, one can also use `run_by` function to prespecify arguments in `tidyverse` pipeline. In the example below `runner` functions are applied on `k = "20 days"` calculated on `"date"` column.

    df %>%
      group_by(group) %>%
      run_by(idx = "date", k = "20 days", na_pad = FALSE) %>%
      mutate(
        cumulative_mse = runner(
          x = .,
          f = function(x) {
            mean((residuals(lm(y ~ x, data = x)))^2)
          }
        ),
        intercept = runner(
          x = .,
          f = function(x) {
            coefficients(lm(y ~ x, data = x))[1]
          }
        ),
        slope = runner(
          x = .,
          f = function(x) {
            coefficients(lm(y ~ x, data = x))[2]
          }
        )
      )

### Parallel mode

The `runner` function can also compute windows in parallel mode. The function doesn’t initialize the parallel cluster automatically but one have to do this outside and pass it to the `runner` through `cl` argument.

    library(parallel)

    numCores <- detectCores()
    cl <- makeForkCluster(numCores)

    runner(
      x = df,
      k = 10,
      idx = "date",
      f = function(x) sum(x$x),
      cl = cl
    )

    stopCluster(cl)

Executing `runner` in parallel mode isn’t always faster than a single thread. Multiple-thread computation generates some overhead due to managing the nodes. In general, complex functions which bases on processor (e.g. loops) used to be quicker in parallel mode but one should assess itself which option has the edge in specific situation.

### Build-in functions

With `runner` one can use any R functions, but some of them are optimized for speed reasons. These functions are:
- aggregating functions - `length_run`, `min_run`, `max_run`, `minmax_run`, `sum_run`, `mean_run`, `streak_run`
- utility functions - `fill_run`, `lag_run`, `which_run`