Model averaging with logistic autoregressive conditional peak over threshold models for regional smog

Abstract

We propose a novel dynamic generalized Pareto distribution (GPD) framework for modeling the time-dependent behavior of the peak over threshold (POT) in extreme smog (PM_2.5) time series. First, unlike static GPD, three dynamic autoregressive conditional generalized Pareto (ACP) models are introduced. Specifically, in these three dynamic models, the exceedances of air pollutant concentration are modeled by a GPD with time-dependent scale and shape parameters conditioned on past PM_2.5 and other air quality factors (SO₂, NO₂, CO) and weather factors (daily average temperature, average relative humidity, average wind speed). Second, unlike the recent studies of ACP models, we impose a logistic function autoregressive structure on the scale and shape parameters of the ACP models, which has simple calculation and flexible modeling for the scale and shape parameters, since the logistic function is used to mean that the changes in the long memory parameter occur in a continuous manner and often applied in time series models. Third, the model averaging method is applied to improve predictive performance using AIC and BIC criteria to select combined weights of the three ACP models. In addition, based on goodness-of-fit tests, the thresholds of the three ACP models are chosen by eight automatic threshold selection procedures to avoid subjectively assigning a certain value as the threshold. Maximum likelihood estimation (MLE) is employed to estimate parameters of the ACP models and its statistical properties are investigated. Various simulation studies and an example of real data in PM_2.5 time series demonstrate the superiority of the proposed ACP models and the stability of the MLE.

Keywords: dynamic autoregressive conditional modeling; generalized Pareto distribution; model averaging; peaks‐over‐threshold; threshold selection.