nufftcf：基于非均匀快速傅里叶变换的非规则采样时间序列自相关与互相关函数快速估计
nufftcf: Fast Auto- and Cross-Correlation Function Estimation for Irregularly-Sampled Time Series via the Non-Uniform FFT
- Université Paris-Saclay（巴黎萨克雷大学）
- CNRS/IN2P3, IJCLab（法国国家科学研究中心/法国核子与粒子物理研究所，IJCLab）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
本研究提出nufftcf工具，通过NUFFT算法实现非规则采样时间序列ACF/CCF的O(n log n)快速估计，经基准测试验证其效率与准确性，可应用于含复杂特征的天文模拟数据。
中文摘要 AI 辅助
估计采样序列的自相关函数（ACF）和互相关函数（CCF）是天文学、环境科学等多个物理领域的标准任务。本研究旨在提供一种专为非规则采样序列设计的ACF/CCF估计器，其数值与已确立且经过充分验证的核加权定义一致，同时实现O(n log n)的时间复杂度，而非O(n²)。nufftcf通过Flatiron研究所的FINUFFT库，利用非均匀快速傅里叶变换（NUFFT）对非规则采样数据计算维纳-辛钦定理，采用高斯和矩形核估计器。算法使用O(n)的双指针扫描替代朴素的O(n²)计算，用于归一化每个滞后区间的有效配对计数。针对小序列的相同估计器的直接实空间实现、作为参考的实现，以及针对规则采样数据的专用经典FFT估计器，均与NUFFT实现共享统一的调用约定。通过合成时间序列，我们验证了nufftcf的ACF性能与地下水时间序列分析领域知名的pastas库相当，CCF性能与天文学时间序列分析领域知名的pyZDCF相当。基准测试确认了预期的渐近缩放：nufftcf的时间复杂度为O(n log n)，而pastas的分箱技术为O(n²)；得益于毫秒级的低开销，nufftcf在中等序列长度时已具备优势。在规则采样数据上，nufftcf的专用FFT路径相比其自身的NUFFT估计器进一步降低了成本和开销。除交叉验证外，我们还在模拟的地基恒星光变曲线上演示了nufftcf的应用，该光曲线结合了准周期旋转信号、相关闪烁噪声、季节性采样间隙和异方差测量误差。
英文摘要
Estimating the auto-correlation function (ACF) and cross-correlation function (CCF) of sampled series is a standard task in many physics fields, including astronomy and environmental sciences. We present nufftcf, an ACF/CCF estimator designed primarily for irregularly sampled series, numerically consistent with established kernel-weighted definitions and scaling as O(nK) for K requested lags, rather than O(n^2). nufftcf was initially developed to evaluate the Wiener-Khinchin theorem for irregularly sampled data using the Non-Uniform Fast Fourier Transform (NUFFT), through the Flatiron Institute FINUFFT library, with Gaussian and rectangle kernels. An O(n)-per-lag two-pointer scan replaces the naive O(n^2) computation of the effective pair count used to normalize each lag bin. This enabled real-space estimators using the same kernels, providing exact reference implementations with the same O(nK) complexity and, in some cases, lower cost than the NUFFT path. The library also provides dedicated classical-FFT estimators for regularly sampled data. All estimators share a common calling convention. Using synthetic time series, we validate nufftcf for ACF against pastas, a library used in groundwater time-series analysis, and for CCF against pyZDCF, used in astronomical time-series analysis. Benchmarks confirm O(nK) scaling for the NUFFT and real-space nufftcf estimators, compared with O(n^2) for the pastas slotting technique. nufftcf is already advantageous at moderate series lengths because of its low millisecond-scale overhead. For regularly sampled data, the FFT path further reduces computational cost. We also demonstrate nufftcf on a simulated ground-based stellar light curve combining quasi-periodic rotation, correlated flicker noise, seasonal sampling gaps, and heteroscedastic measurement errors. Notebooks and scripts are provided to reproduce the examples and explore other use cases.
