Nonlinear Sciences - Adaptation and Self-Organizing Systems, Nonlinear Sciences - Chaotic Dynamics, Physics - Data Analysis, Statistics and Probability, Physics - Geophysics

The resilience, or stability, of major Earth system components is increasingly threatened by anthropogenic pressures, demanding reliable early warning signals for abrupt and irreversible regime shifts. Widely used data-driven resilience indicators based on variance and autocorrelation detect `critical slowing down', a signature of decreasing stability. However, the interpretation of these indicators is hampered by poorly understood interdependencies and their susceptibility to common data issues such as missing values and outliers. Here, we establish a rigorous mathematical analysis of the statistical dependency between variance- and autocorrelation-based resilience indicators, revealing that their agreement is fundamentally driven by the time series' initial data point. Using synthetic and empirical data, we demonstrate that missing values substantially weaken indicator agreement, while outliers introduce systematic biases that lead to overestimation of resilience based on temporal autocorrelation. Our results provide a necessary and rigorous foundation for preprocessing strategies and accuracy assessments across the growing number of disciplines that use real-world data to infer changes in system resilience.