Distribution shifts in time-series data are complex due to temporal dependencies, multivariable interactions, and trend changes. However, robust methods often rely on structural assumptions that lack thorough empirical validation, limiting their practical applicability. In order to support an empirically grounded inductive approach to research, we introduce our Time-Series Shift Attribution (TSSA) framework, which analyzes problem-specific patterns of distribution shifts. Our framework attributes performance degradation from various types of shifts to each temporal data property in a detailed manner, supported by theoretical analysis of unbiasedness and asymptotic properties. Empirical studies in real-world healthcare applications highlight how the TSSA framework enhances the understanding of time-series shifts, facilitating reliable model deployment and driving targeted improvements from both algorithmic and data-centric perspectives.