Percentile-Based Slope-Constrained Linear Interpolation for Robust Imputation of Highly Volatile PM2.5 Time Series

Reliable reconstruction of missing observations is essential for environmental time-series analysis, particularly for highly volatile air-quality indicators such as PM2.5. Although linear interpolation is widely used for short-gap imputation due to its simplicity and computational efficiency, it does not explicitly regulate slope dynamics and may produce physically implausible transitions in rapidly fluctuating data. This study proposes a percentile-based slope-constrained linear interpolation method that estimates a slope threshold from the empirical distribution of historical first-order differences and applies a sequential constraint during interpolation to prevent unrealistic gradient changes. The approach requires only a single data-driven parameter and maintains linear computational complexity. • Data-driven slope threshold estimated from the percentile distribution of historical first-order differences. • Sequential slope constraint applied to prevent unrealistic gradient transitions during interpolation. • Linear-time method that preserves the simplicity of standard interpolation while improving reconstruction accuracy.