Data gaps and outliers distort critical-slowing-down-based resilience indicators

The resilience of natural systems, such as climate or ecosystems, is increasingly threatened by anthropogenic pressures, making it essential to quantify resilience changes before abrupt and irreversible regime shifts occur. Widely used data-driven resilience indicators based on variance and autocorrelation detect "critical slowing down," a signature of decreasing stability and possible impending critical transitions in dynamical systems with alternative equilibria. However, the interpretation of these indicators is complicated by common data issues such as missing values and outliers, whose effects remain poorly understood. Here, we develop a general mathematical framework that rigorously characterizes 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 the agreement of resilience indicators, 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 empirical data to infer changes in system resilience.