# Percentile-based slope-constrained linear interpolation for robust imputation of highly volatile PM2.5 time series

## TL;DR

This paper introduces a new interpolation method for PM2.5 data that improves accuracy by constraining unrealistic slope changes.

## Contribution

A novel percentile-based slope-constrained linear interpolation method is proposed for robust PM2.5 time series imputation.

## Key findings

- A data-driven slope threshold is estimated from historical first-order differences.
- Sequential slope constraints prevent unrealistic gradient transitions during interpolation.
- The method maintains linear computational complexity while improving reconstruction accuracy.

## Abstract

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.

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.

Image, graphical abstract