PM 2.5 air quality index in major cities. long memory analysis with fractional integration

Abstract

This article presents new evidence on the persistence, seasonality, and trends of fine particulate matter (PM2.5) Air Quality Index (AQI) across twenty global megacities from January 2014 to January 2026. The research applies a fractional integration approach to model the long-memory dynamics using high-frequency daily data. Rather than relying on standard binary unit root tests, we adopt the fractional integration framework, which provides a continuous measure of the degree of persistence. Robustness checks include the evaluation of both parametric and semiparametric estimators, analysis of structural breaks, potential impacts of interpolation and the effects of outliers. The results reveal that air quality dynamics follow an I(d) fractional behaviour in all cases, with higher persistence (0.50 < d < 0.65) in cities with wet/dry seasons; and lower levels (0.15 < d < 0.30) in cities with a more distributed pattern of precipitation across the year. Furthermore, cities with lower quality levels (e.g. Mumbai, New Delhi, Kolkata, and Dhaka) also exhibit the highest levels of persistence and, as a result, prolonged risk of extreme episodes. Extensive robustness checks confirm these results, though they reveal a localized sensitivity linked to large data gaps combined with internal outliers.