Quantile Trend Regression and Its Application to Central England Temperature

Harry Haupt,Markus Fritsch

doi:10.3390/math10030413

Abstract

The identification and estimation of trends in hydroclimatic time series remains an important task in applied climate research. The statistical challenge arises from the inherent nonlinearity, complex dependence structure, heterogeneity and resulting non-standard distributions of the underlying time series. Quantile regressions are considered an important modeling technique for such analyses because of their rich interpretation and their broad insensitivity to extreme distributions. This paper provides an asymptotic justification of quantile trend regression in terms of unknown heterogeneity and dependence structure and the corresponding interpretation. An empirical application sheds light on the relevance of quantile regression modeling for analyzing monthly Central England temperature anomalies and illustrates their various heterogenous trends. Our results suggest the presence of heterogeneities across the considered seasonal cycle and an increase in the relative frequency of observing unusually high temperatures.

Highlights

The current phase of rapidly accelerating impacts of global warming reveals many immediate effects on direct and indirect threats to global health and clearly illustrates the role of human activities (e.g., [1,2])
Rivas and Gonzalo [6] provide a definition of global warming and trending time series and present evidence for warming based on the Central England Temperature (CET) and global temperature time series
Our results are in accordance with earlier literature, which provided evidence for global warming and trending in temperature time series and noted heterogeneity across the different months (e.g., [4,6,28])

Summary

Introduction

The current phase of rapidly accelerating impacts of global warming reveals many immediate effects on direct and indirect threats to global health and clearly illustrates the role of human activities (e.g., [1,2]). Substantial increases in mean temperatures across the world and heterogeneity in temperature increases across months are noted in Vogelsang and Franses [4], who emphasize that especially winters are warming in the northern hemisphere. King et al [1] document substantial warming in the Central England Temperature (CET) time series for 2014 based on simulated and observed datasets and provide evidence for a human-induced increase in the relative frequency of observing record high temperatures. King [5] extends their previous analysis beyond the univariate approach and provides a proxy for the local response to global warming by modeling local temperature as a nonlinear parametric function of global temperature. Rivas and Gonzalo [6] provide a definition of global warming and trending time series and present evidence for warming based on the CET and global temperature time series

Objectives

Methods

Results

Conclusion