Statistics

algorithms
r
Author

Jason Foster

Published

November 23, 2025

Usage

library(roll)
library(microbenchmark)
options(microbenchmark.unit = "us")
n_vars <- 10
n_obs <- 1000
weights <- 0.9 ^ (n_obs:1)

x <- matrix(rnorm(n_obs * n_vars), nrow = n_obs, ncol = n_vars)
y <- matrix(rnorm(n_obs), nrow = n_obs, ncol = 1)
x_lgl <- x < 0

Rolling any

result <- microbenchmark("125" = roll_any(x_lgl, width = 125, min_obs = 1),
                         "250" = roll_any(x_lgl, width = 250, min_obs = 1),
                         "500" = roll_any(x_lgl, width = 500, min_obs = 1),
                         "1000" = roll_any(x_lgl, width = 1000, min_obs = 1))
print(result)
Unit: microseconds
 expr   min     lq    mean median     uq    max neval
  125  89.9 143.60 158.607 155.50 172.30  218.2   100
  250 117.5 139.65 153.598 149.80 162.70  210.3   100
  500 105.7 141.20 164.751 154.10 167.25 1000.0   100
 1000  83.0 126.95 142.486 135.75 155.55  219.8   100

Rolling all

result <- microbenchmark("125" = roll_all(x_lgl, width = 125, min_obs = 1),
                         "250" = roll_all(x_lgl, width = 250, min_obs = 1),
                         "500" = roll_all(x_lgl, width = 500, min_obs = 1),
                         "1000" = roll_all(x_lgl, width = 1000, min_obs = 1))
print(result)
Unit: microseconds
 expr  min    lq    mean median     uq   max neval
  125 83.3 92.50 105.384  95.85 101.65 181.5   100
  250 84.0 89.60 105.699  93.75 106.25 200.2   100
  500 78.0 87.20 104.185  90.90 109.25 284.4   100
 1000 74.3 80.35  89.024  82.40  88.40 177.2   100

Rolling sums

\[ \begin{aligned} &\text{Expanding window} \\ &\bullet\text{sum}_{x}\leftarrow\lambda\times\text{sum}_{x}+\text{w}_{new}\times\text{x}_{new}\\ &\text{Rolling window}\\ &\bullet\text{sum}_{x}\leftarrow\lambda\times\text{sum}_{x}+\text{w}_{new}\times\text{x}_{new}-\lambda\times\text{w}_{old}\times\text{x}_{old} \end{aligned} \]

result <- microbenchmark("125" = roll_sum(x, width = 125, min_obs = 1, weights = weights),
                         "250" = roll_sum(x, width = 250, min_obs = 1, weights = weights),
                         "500" = roll_sum(x, width = 500, min_obs = 1, weights = weights),
                         "1000" = roll_sum(x, width = 1000, min_obs = 1, weights = weights))
print(result)
Unit: microseconds
 expr  min     lq    mean median     uq   max neval
  125 92.3 105.80 130.447 116.80 144.75 253.3   100
  250 95.0 104.85 126.861 113.35 137.15 273.7   100
  500 91.7 102.65 123.558 111.90 130.20 286.9   100
 1000 88.5  99.10 123.163 107.45 140.50 227.8   100

Rolling products

\[ \begin{aligned} &\text{Expanding window}\\ &\bullet\text{prod}_{w}\leftarrow\text{prod}_{w}\times\text{w}_{new}\\ &\bullet\text{prod}_{x}\leftarrow\text{prod}_{x}\times\text{x}_{new}\\ &\text{Rolling window}\\ &\bullet\text{prod}_{x}\leftarrow\text{prod}_{x}\times\text{x}_{new}/\text{x}_{old} \end{aligned} \]

result <- microbenchmark("125" = roll_prod(x, width = 125, min_obs = 1, weights = weights),
                         "250" = roll_prod(x, width = 250, min_obs = 1, weights = weights),
                         "500" = roll_prod(x, width = 500, min_obs = 1, weights = weights),
                         "1000" = roll_prod(x, width = 1000, min_obs = 1, weights = weights))
print(result)
Unit: microseconds
 expr   min     lq    mean median     uq   max neval
  125 204.7 219.35 241.780 234.20 246.50 387.8   100
  250 207.3 221.75 253.678 234.35 259.70 610.5   100
  500 139.8 152.10 173.136 167.15 185.20 266.8   100
 1000 135.7 148.45 166.439 162.10 174.35 271.4   100

Rolling means

\[ \begin{aligned} &\text{Expanding window}\\ &\bullet\text{sum}_{w}\leftarrow\text{sum}_{w}+\text{w}_{new}\\ &\bullet\text{sum}_{x}\leftarrow\lambda\times\text{sum}_{x}+\text{w}_{new}\times\text{x}_{new}\\ &\text{Rolling window}\\ &\bullet\text{sum}_{x}\leftarrow\lambda\times\text{sum}_{x}+\text{w}_{new}\times\text{x}_{new}-\lambda\times\text{w}_{old}\times \text{x}_{old} \end{aligned} \]

result <- microbenchmark("125" = roll_mean(x, width = 125, min_obs = 1, weights = weights),
                         "250" = roll_mean(x, width = 250, min_obs = 1, weights = weights),
                         "500" = roll_mean(x, width = 500, min_obs = 1, weights = weights),
                         "1000" = roll_mean(x, width = 1000, min_obs = 1, weights = weights))
print(result)
Unit: microseconds
 expr   min     lq    mean median     uq   max neval
  125  93.0 109.80 129.285 116.10 152.35 216.7   100
  250 101.5 110.35 132.540 118.95 151.65 355.6   100
  500  96.0 108.40 130.634 115.35 153.00 232.8   100
 1000  92.0 102.25 124.633 112.05 147.90 232.1   100

Rolling minimums

result <- microbenchmark("125" = roll_min(x, width = 125, min_obs = 1, weights = weights),
                         "250" = roll_min(x, width = 250, min_obs = 1, weights = weights),
                         "500" = roll_min(x, width = 500, min_obs = 1, weights = weights),
                         "1000" = roll_min(x, width = 1000, min_obs = 1, weights = weights))
print(result)
Unit: microseconds
 expr   min     lq    mean median     uq   max neval
  125 106.2 116.80 139.655 124.25 145.55 231.4   100
  250 101.6 115.55 139.389 123.45 157.75 240.4   100
  500 102.6 113.20 136.138 124.00 133.10 301.6   100
 1000 103.2 116.55 137.804 128.15 154.25 227.3   100

Rolling maximums

result <- microbenchmark("125" = roll_max(x, width = 125, min_obs = 1, weights = weights),
                         "250" = roll_max(x, width = 250, min_obs = 1, weights = weights),
                         "500" = roll_max(x, width = 500, min_obs = 1, weights = weights),
                         "1000" = roll_max(x, width = 1000, min_obs = 1, weights = weights))
print(result)
Unit: microseconds
 expr   min     lq    mean median     uq   max neval
  125 104.9 123.35 155.302 140.35 180.35 287.7   100
  250 106.4 123.60 157.260 137.30 188.45 309.5   100
  500 108.3 123.25 151.723 131.10 170.30 415.7   100
 1000 107.7 122.50 160.164 143.10 190.95 341.3   100

Rolling index of minimums

result <- microbenchmark("125" = roll_idxmin(x, width = 125, min_obs = 1, weights = weights),
                         "250" = roll_idxmin(x, width = 250, min_obs = 1, weights = weights),
                         "500" = roll_idxmin(x, width = 500, min_obs = 1, weights = weights),
                         "1000" = roll_idxmin(x, width = 1000, min_obs = 1, weights = weights))
print(result)
Unit: microseconds
 expr   min     lq    mean median     uq   max neval
  125 103.0 133.35 164.849 158.10 189.80 375.4   100
  250 104.4 132.20 160.987 160.90 181.05 306.5   100
  500 104.3 125.25 159.586 151.00 180.95 348.4   100
 1000  94.6 131.20 158.884 156.75 180.40 365.6   100

Rolling index of maximums

result <- microbenchmark("125" = roll_idxmax(x, width = 125, min_obs = 1, weights = weights),
                         "250" = roll_idxmax(x, width = 250, min_obs = 1, weights = weights),
                         "500" = roll_idxmax(x, width = 500, min_obs = 1, weights = weights),
                         "1000" = roll_idxmax(x, width = 1000, min_obs = 1, weights = weights))
print(result)
Unit: microseconds
 expr   min     lq    mean median     uq   max neval
  125 108.1 128.95 158.456 149.75 180.05 310.0   100
  250 102.0 130.25 154.937 151.95 170.40 278.5   100
  500 106.6 121.95 149.305 141.75 174.35 243.6   100
 1000 102.9 119.20 144.368 138.60 159.90 244.5   100

Rolling medians

# "'online' is only supported for equal 'weights'"
result <- microbenchmark("125" = roll_median(x, width = 125, min_obs = 1),
                         "250" = roll_median(x, width = 250, min_obs = 1),
                         "500" = roll_median(x, width = 500, min_obs = 1),
                         "1000" = roll_median(x, width = 1000, min_obs = 1))
print(result)
Unit: microseconds
 expr   min     lq    mean median     uq    max neval
  125 772.5 807.95 833.559 831.10 845.40 1283.9   100
  250 749.9 803.20 817.830 817.35 833.55  871.3   100
  500 719.1 746.15 864.045 766.05 784.65 5572.8   100
 1000 544.9 567.45 615.572 584.50 603.45 2154.4   100

Rolling quantiles

# "'online' is only supported for equal 'weights'"
result <- microbenchmark("125" = roll_quantile(x, width = 125, min_obs = 1),
                         "250" = roll_quantile(x, width = 250, min_obs = 1),
                         "500" = roll_quantile(x, width = 500, min_obs = 1),
                         "1000" = roll_quantile(x, width = 1000, min_obs = 1))
print(result)
Unit: microseconds
 expr   min     lq    mean median     uq    max neval
  125 879.4 896.85 924.384 915.75 944.15 1217.5   100
  250 863.5 880.90 912.054 907.50 930.65 1039.5   100
  500 799.9 817.65 847.926 844.05 865.90  993.8   100
 1000 614.1 628.35 657.674 657.60 682.85  718.3   100

Rolling variances

\[ \begin{aligned} &\text{Expanding window}\\ &\bullet\text{sum}_{w}\leftarrow\text{sum}_{w}+\text{w}_{new}\\ &\bullet\text{sumsq}_{w}\leftarrow\text{sumsq}_{w}+\text{w}_{new}^{2}\\ &\bullet\text{sumsq}_{x}\leftarrow\lambda\times\text{sumsq}_{x}+\text{w}_{new}\times (\text{x}_{new}-\text{mean}_{x})(\text{x}_{new}-\text{mean}_{prev_x})\\ &\text{Rolling window}\\ &\bullet\text{sumsq}_{x}\leftarrow\lambda\times\text{sumsq}_{x}+\text{w}_{new}\times (\text{x}_{new}-\text{mean}_{x})(\text{x}_{new}-\text{mean}_{prev_x})-\\ &\lambda\times\text{w}_{old}\times (\text{x}_{old}-\text{mean}_{x})(\text{x}_{old}-\text{mean}_{prev_x}) \end{aligned} \]

result <- microbenchmark("125" = roll_var(x, width = 125, min_obs = 1, weights = weights),
                         "250" = roll_var(x, width = 250, min_obs = 1, weights = weights),
                         "500" = roll_var(x, width = 500, min_obs = 1, weights = weights),
                         "1000" = roll_var(x, width = 1000, min_obs = 1, weights = weights))
print(result)
Unit: microseconds
 expr   min     lq    mean median     uq   max neval
  125 118.9 138.75 147.525 146.55 153.25 239.9   100
  250 114.7 136.15 152.035 145.30 157.50 310.6   100
  500 113.0 135.45 145.732 142.10 149.70 396.2   100
 1000 106.5 123.95 139.719 130.85 137.90 641.3   100

Rolling standard deviations

result <- microbenchmark("125" = roll_sd(x, width = 125, min_obs = 1, weights = weights),
                         "250" = roll_sd(x, width = 250, min_obs = 1, weights = weights),
                         "500" = roll_sd(x, width = 500, min_obs = 1, weights = weights),
                         "1000" = roll_sd(x, width = 1000, min_obs = 1, weights = weights))
print(result)
Unit: microseconds
 expr   min     lq    mean median    uq   max neval
  125 121.3 142.10 152.207 147.20 156.0 282.4   100
  250 119.7 139.50 153.363 145.30 156.8 395.7   100
  500 128.2 136.00 148.320 141.70 149.6 270.2   100
 1000 109.7 130.95 140.115 136.65 143.7 287.5   100

Rolling scaling and centering

result <- microbenchmark("125" = roll_scale(x, width = 125, min_obs = 1, weights = weights),
                         "250" = roll_scale(x, width = 250, min_obs = 1, weights = weights),
                         "500" = roll_scale(x, width = 500, min_obs = 1, weights = weights),
                         "1000" = roll_scale(x, width = 1000, min_obs = 1, weights = weights))
print(result)
Unit: microseconds
 expr   min     lq    mean median     uq    max neval
  125 147.0 151.90 162.812 156.35 162.00  330.4   100
  250 142.5 152.75 208.041 159.55 171.80 3517.7   100
  500 140.3 149.00 164.837 156.00 165.75  321.4   100
 1000 135.9 140.60 151.609 146.15 151.80  267.4   100

Rolling covariances

\[ \begin{aligned} &\text{Expanding window}\\ &\bullet\text{sum}_{w}\leftarrow\text{sum}_{w}+\text{w}_{new}\\ &\bullet\text{sumsq}_{w}\leftarrow\text{sumsq}_{w}+\text{w}_{new}^{2}\\ &\bullet\text{sumsq}_{xy}\leftarrow\lambda\times\text{sumsq}_{xy}+\text{w}_{new}\times (\text{x}_{new}-\text{mean}_{x})(\text{y}_{new}-\text{mean}_{prev_y})\\ &\text{Rolling window}\\ &\bullet\text{sumsq}_{xy}\leftarrow\lambda\times\text{sumsq}_{xy}+\text{w}_{new}\times (\text{x}_{new}-\text{mean}_{x})(\text{y}_{new}-\text{mean}_{prev_y})-\\ &\lambda\times\text{w}_{old}\times (\text{x}_{old}-\text{mean}_{x})(\text{y}_{old}-\text{mean}_{prev_y}) \end{aligned} \]

result <- microbenchmark("125" = roll_cov(x, width = 125, min_obs = 1, weights = weights),
                         "250" = roll_cov(x, width = 250, min_obs = 1, weights = weights),
                         "500" = roll_cov(x, width = 500, min_obs = 1, weights = weights),
                         "1000" = roll_cov(x, width = 1000, min_obs = 1, weights = weights))
print(result)
Unit: microseconds
 expr   min     lq     mean median      uq    max neval
  125 724.4 906.60  968.837 983.15 1018.15 1164.9   100
  250 724.5 881.15 1045.220 942.70  990.00 6748.3   100
  500 677.5 820.30  960.156 867.15  929.85 6220.2   100
 1000 613.7 739.35  828.754 770.95  834.35 5979.7   100

Rolling correlations

result <- microbenchmark("125" = roll_cor(x, width = 125, min_obs = 1, weights = weights),
                         "250" = roll_cor(x, width = 250, min_obs = 1, weights = weights),
                         "500" = roll_cor(x, width = 500, min_obs = 1, weights = weights),
                         "1000" = roll_cor(x, width = 1000, min_obs = 1, weights = weights))
print(result)
Unit: microseconds
 expr   min      lq     mean  median      uq    max neval
  125 862.8 1014.30 1093.189 1096.25 1165.60 1298.5   100
  250 841.3  968.30 1121.754 1063.50 1115.20 4588.4   100
  500 788.5  906.80 1027.385  986.30 1083.00 4503.5   100
 1000 688.6  801.25  915.180  846.25  896.05 4321.1   100

Rolling crossproducts

result <- microbenchmark("125" = roll_crossprod(x, width = 125, min_obs = 1, weights = weights),
                         "250" = roll_crossprod(x, width = 250, min_obs = 1, weights = weights),
                         "500" = roll_crossprod(x, width = 500, min_obs = 1, weights = weights),
                         "1000" = roll_crossprod(x, width = 1000, min_obs = 1, weights = weights))
print(result)
Unit: microseconds
 expr   min    lq    mean median     uq    max neval
  125 595.0 651.5 713.679 710.20 767.80  875.7   100
  250 592.1 637.3 727.521 690.80 748.55 4091.1   100
  500 574.7 624.7 759.912 715.65 739.85 4138.6   100
 1000 529.9 564.7 684.105 589.80 674.30 4107.4   100

Rolling linear models

\[ \begin{aligned} &\text{coef}=\text{cov}_{xx}^{-1}\times\text{cov}_{xy}\\ &\text{intercept}=\text{mean}_{y}-\text{coef}\times\text{mean}_{x}\\ &\text{rsq}=\frac{\text{coef}^{T}\times\text{cov}_{xx}\times\text{coef}}{\text{var}_{y}}\\ &\text{var}_{resid}=\frac{(1-\text{rsq})(\text{var}_{y})(\text{sum}_{w}-\text{sumsq}_{w}/\text{sum}_{w})}{\text{n}_{rows}-\text{n}_{cols}}\\ &\text{xx}=\text{cov}_{xx}\times(\text{sum}_{w}-\text{sumsq}_{w}/\text{sum}_{w})\\ &\text{se}_{coef}=\sqrt{\text{var}_{resid}\times\text{diag}(\text{xx}^{-1})}\\ &\text{se}_{intercept}=\sqrt{\text{var}_{resid}\left(1/\text{sum}_{w}+\text{mean}_{x}^{T}\text{xx}^{-1}\text{mean}_{x}\right)} \end{aligned} \]

result <- microbenchmark("125" = roll_lm(x, y, width = 125, min_obs = 1, weights = weights),
                         "250" = roll_lm(x, y, width = 250, min_obs = 1, weights = weights),
                         "500" = roll_lm(x, y, width = 500, min_obs = 1, weights = weights),
                         "1000" = roll_lm(x, y, width = 1000, min_obs = 1, weights = weights))
print(result)
Unit: microseconds
 expr    min      lq     mean  median      uq    max neval
  125 2190.5 2401.40 2549.411 2498.90 2593.55 3943.7   100
  250 2193.5 2334.05 2565.596 2493.55 2627.20 6566.8   100
  500 2111.9 2338.05 2567.908 2428.40 2577.60 6740.5   100
 1000 2037.4 2267.00 2533.283 2398.95 2546.65 6696.1   100

References