robustrolling

High-performance rolling-window statistics for R and Python — eleven algorithms implemented in C++17, exposed through idiomatic bindings in both languages, with O(1) or O(log w) updates per element.

API Reference

Algorithm overview

C++ class

Algorithm

Complexity

R function(s)

Python class / function(s)

SlidingMean

Prefix sum + SIMD

O(n) batch

rolling_mean

rolling_mean, SlidingMean

SlidingWelfordRing

Welford online variance (ring buffer)

O(1)

rolling_variance (method="stable")

rolling_variance, SlidingWelford

SlidingMomentsPrefix

Prefix sums of raw moments

O(n) batch

rolling_variance/skewness/kurtosis (method="fast")

SlidingMomentsPrefix

MonotonicMax

Monotonic deque maximum

O(1) amortised

rolling_max

rolling_max, MonotonicMax

MonotonicMin

Monotonic deque minimum

O(1) amortised

rolling_min

rolling_min, MonotonicMin

SlidingMedian

Auto-dispatches to one of three below

—

rolling_median (expect_nan=)

rolling_median, SlidingMedian

FlatMedian

Sorted std::vector + binary search

O(w) insert

—

FlatMedian

MultisetMedian

std::multiset + tracked iterator

O(log w)

—

MultisetMedian

TwoHeapMedian

Two heaps + lazy deletion

O(log w)

—

TwoHeapMedian

SlidingMoments

Terriberry 4th-moment online algorithm

O(1)

rolling_skewness, rolling_kurtosis (method="stable")

rolling_skewness, rolling_kurtosis, SlidingMoments

SlidingCovariance

2-D Welford online covariance

O(1)

rolling_cov, rolling_cor

rolling_cov, rolling_cor, SlidingCovariance

Performance

Benchmarked on Apple M-series (ARM), window = 100, n = 1 000 000 (median of 10 runs).

Python vs pandas

Function

robustrolling

pandas

speedup

rolling_mean

3.1 ms

4.4 ms

1.4x

rolling_max

11.1 ms

11.7 ms

1.1x

rolling_min

11.2 ms

12.2 ms

1.1x

rolling_median

106 ms

233 ms

2.2x

rolling_variance

15.2 ms

9.6 ms

0.6x

rolling_skewness

14.0 ms

9.1 ms

0.6x

rolling_kurtosis

14.3 ms

9.2 ms

0.6x

rolling_cov

14.8 ms

18.2 ms

1.2x

rolling_cor

14.6 ms

36.7 ms

2.5x

Python vs Polars

rolling_median uses FlatMedian at window ≤ 600; TwoHeapMedian wins at large windows where Polars’ fixed O(w) algorithm loses ground.

Function

robustrolling

Polars

speedup

rolling_mean

3.1 ms

8.0 ms

2.6x

rolling_max

11.1 ms

11.4 ms

1.0x

rolling_min

11.0 ms

11.6 ms

1.1x

rolling_median

55 ms

41 ms

0.7x (w=100)

rolling_variance

15.7 ms

16.2 ms

1.0x

rolling_skewness

13.9 ms

16.0 ms

1.2x

rolling_kurtosis

14.3 ms

15.6 ms

1.1x

Python — stable vs fast (prefix-sum acceleration)

Function

stable

fast

speedup

mean (assume_finite)

3.2 ms

0.73 ms

4.4x

variance

15.2 ms

3.9 ms

3.9x

skewness

13.9 ms

10.0 ms

1.4x

kurtosis

14.4 ms

7.6 ms

1.9x

R vs slider vs RcppRoll

Function

robustrolling

slider

RcppRoll

vs slider

vs RcppRoll

rolling_max

15.1 ms

338 ms

175 ms

22x

12x

rolling_min

14.9 ms

350 ms

175 ms

24x

12x

rolling_mean

3.1 ms

1 523 ms

37.4 ms

487x

12x

rolling_variance

16.0 ms

2 477 ms

304 ms

154x

19x

rolling_median

112 ms

10 084 ms

1 938 ms

90x

17x

R — stable vs fast

Function

stable

fast

speedup

mean (assume_finite)

3.2 ms

0.78 ms

4.0x

variance

16.2 ms

4.1 ms

4.0x

skewness

14.5 ms

10.3 ms

1.4x

kurtosis

14.4 ms

7.8 ms

1.8x

Install for R

# Requires R ≥ 4.0 and a C++17 compiler
install.packages("remotes")
remotes::install_github("IgorPtak/rolling_window")

Install for Python

# Requires Python ≥ 3.10 and a C++17 compiler
pip install git+https://github.com/IgorPtak/rolling_window.git#subdirectory=py_package

# Or clone and install locally:
git clone https://github.com/IgorPtak/rolling_window.git
pip install rolling_window/py_package/