A Missing Tool for Calculating the Auto/Cross-correlation Functions under Nonuniform Sampling Observations
9 affiliations
- 1Nanjing University
- 2Key Laboratory of Modern Astronomy and Astrophysics (Nanjing University)
- 3Chinese Academy of Sciences
- 4Nanjing University of Information Science and Technology
- 5Guangxi University
- 6Beijing Normal University
- 7Xinjiang Astronomical Observatory
- 8Xinjiang Key Laboratory of Radio Astrophysics
- 9Zhengzhou University
Abstract
Nonuniform sampling presents a long-standing challenge in astrophysical time-domain analysis, invalidating the standard autocorrelation and cross-correlation functions and forcing researchers to adopt ad hoc methods like interpolation or binning, which introduce unquantified biases and lack rigorous error estimation. Here, we introduce a new method for calculating the nonuniform autocorrelation function (NUACF) and nonuniform cross-correlation function (NUCCF) for irregularly sampled time series. Instead of relying on interpolation, it naturally evaluates the correlation function by incorporating time-interval weights and misalignment penalties. Monte Carlo simulations provide confidence bands for significance assessment and a complete error budget for the time delays that accounts for both flux uncertainties and sampling irregularity (essential but generally absent from existing methods). Through extensive simulations, we demonstrate that our method outperforms traditional methods across various conditions, from strictly periodic to complex repeating variability patterns (e.g., intermittent but aperiodic). Its effectiveness is demonstrated via various real astrophysical data sets, revealing repetitive variability in stellar light curves, measuring time delays for multiband disk reverberation in the active galactic nucleus Fairall 9, and providing model-independent validation of time delays for the gravitationally lensed quasar HE 0435-1223. The method provides a rigorous and general solution to the ubiquitous problem of nonuniform sampling, positioning it as a useful tool for large-scale time-domain survey data analysis. The framework is also directly applicable to emerging time-domain phenomena such as fast radio bursts (FRBs), enabling, for example, the study of correlations between persistent radio source luminosity and repeating FRB activity, or among the multiparameter variability curves of FRB emission itself.
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BibTeX
@article{胡2026missing,
title = {{A Missing Tool for Calculating the Auto/Cross-correlation Functions under Nonuniform Sampling Observations}},
author = {Chen-Ran 宸然 Hu 胡 and Yong-Feng 永锋 Huang 黄 and Jin-Jun 金军 Geng 耿 and Orkash 热卡西·艾麦提 Amat 吾 and Ze-Cheng 泽城 Zou 邹 and Chen 晨 Deng 邓 and Fan 帆 Xu 许 and Xiao-Fei 小飞 Dong 董 and Chen 琛 Du 杜 and Nurimangul 尔曼古丽·努尔麦麦提 Nurmamat 努 and Pei 培 Wang 王 and Lang 朗 Cui 崔 and Cheng-Ming 程明 Li 李},
journal = {The Astrophysical Journal Supplement Series},
year = {2026},
month = oct,
doi = {10.3847/1538-4365/aeac17},
url = {https://iopscience.iop.org/article/10.3847/1538-4365/aeac17},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - A Missing Tool for Calculating the Auto/Cross-correlation Functions under Nonuniform Sampling Observations
AU - Chen-Ran 宸然 Hu 胡
AU - Yong-Feng 永锋 Huang 黄
AU - Jin-Jun 金军 Geng 耿
AU - Orkash 热卡西·艾麦提 Amat 吾
AU - Ze-Cheng 泽城 Zou 邹
AU - Chen 晨 Deng 邓
AU - Fan 帆 Xu 许
AU - Xiao-Fei 小飞 Dong 董
AU - Chen 琛 Du 杜
AU - Nurimangul 尔曼古丽·努尔麦麦提 Nurmamat 努
AU - Pei 培 Wang 王
AU - Lang 朗 Cui 崔
AU - Cheng-Ming 程明 Li 李
PY - 2026
DA - 2026/10/30
JO - The Astrophysical Journal Supplement Series
DO - 10.3847/1538-4365/aeac17
UR - https://iopscience.iop.org/article/10.3847/1538-4365/aeac17
AB - Nonuniform sampling presents a long-standing challenge in astrophysical time-domain analysis, invalidating the standard autocorrelation and cross-correlation functions and forcing researchers to adopt ad hoc methods like interpolation or binning, which introduce unquantified biases and lack rigorous error estimation. Here, we introduce a new method for calculating the nonuniform autocorrelation function (NUACF) and nonuniform cross-correlation function (NUCCF) for irregularly sampled time series. Instead of relying on interpolation, it naturally evaluates the correlation function by incorporating time-interval weights and misalignment penalties. Monte Carlo simulations provide confidence bands for significance assessment and a complete error budget for the time delays that accounts for both flux uncertainties and sampling irregularity (essential but generally absent from existing methods). Through extensive simulations, we demonstrate that our method outperforms traditional methods across various conditions, from strictly periodic to complex repeating variability patterns (e.g., intermittent but aperiodic). Its effectiveness is demonstrated via various real astrophysical data sets, revealing repetitive variability in stellar light curves, measuring time delays for multiband disk reverberation in the active galactic nucleus Fairall 9, and providing model-independent validation of time delays for the gravitationally lensed quasar HE 0435-1223. The method provides a rigorous and general solution to the ubiquitous problem of nonuniform sampling, positioning it as a useful tool for large-scale time-domain survey data analysis. The framework is also directly applicable to emerging time-domain phenomena such as fast radio bursts (FRBs), enabling, for example, the study of correlations between persistent radio source luminosity and repeating FRB activity, or among the multiparameter variability curves of FRB emission itself.
SN - 0067-0049
SN - 1538-4365
ER -