nufftcf: Fast Auto- and Cross-Correlation Function Estimation for Irregularly-Sampled Time Series via the Non-Uniform FFT

Abstract

Estimating the auto-correlation function (ACF) and the cross-correlation function (CCF) of sampled series is a standard task across different physics fields, such as astronomy, and environmental sciences. We aim to provide an ACF/CCF estimator primarily designed for irregularly sampled series that is numerically consistent with established, well-validated kernel-weighted definitions, while scaling as O(n log n) rather than O(n^2). nufftcf evaluates the Wiener-Khinchin theorem for irregularly sampled data using the Non-Uniform Fast Fourier Transform (NUFFT), via the Flatiron Institute's FINUFFT library, and using Gaussian and rectangular kernel estimators. An O(n) two-pointer scan replaces the naive O(n^2) computation of the effective pair count that normalizes each lag bin. Direct, real-space implementations of the same estimators for small series and for reference, and dedicated classical-FFT estimators for regularly sampled data, are provided alongside the NUFFT implementation, all sharing a single calling convention. With synthetic time series, we validate nufftcf for ACF against pastas, a library known in groundwater time series analysis, and for CCF against pyZDCF, known in astronomical time series analysis. Benchmarks confirm the expected asymptotic scalings: O(n log n) for nufftcf versus O(n^2) for the pastas slotting technique, with nufftcf already advantageous at moderate series lengths thanks to its low (millisecond-scale) overhead. On regularly sampled data, nufftcf's dedicated FFT path further reduces both cost and overhead relative to its own NUFFT estimator. Beyond this cross-validation exercise, we further demonstrate nufftcf on a simulated ground-based stellar light curve combining a quasi-periodic rotation signal, correlated flicker noise, seasonal sampling gaps, and heteroscedastic measurement errors.