Autoregressive Wild Bootstrap Inference for Nonparametric Trends

TL;DR

This paper introduces an autoregressive wild bootstrap method for constructing confidence bands around smooth trends, effectively handling missing data, serial dependence, and heteroskedasticity, with applications in climatology.

Contribution

It presents a new bootstrap approach that is easy to implement and robust to missing data, with proven asymptotic validity for trend inference.

Findings

Method performs well in simulations.

Successfully applied to atmospheric ethane data.

Handles missing data without adjustments.

Abstract

In this paper we propose an autoregressive wild bootstrap method to construct confidence bands around a smooth deterministic trend. The bootstrap method is easy to implement and does not require any adjustments in the presence of missing data, which makes it particularly suitable for climatological applications. We establish the asymptotic validity of the bootstrap method for both pointwise and simultaneous confidence bands under general conditions, allowing for general patterns of missing data, serial dependence and heteroskedasticity. The finite sample properties of the method are studied in a simulation study. We use the method to study the evolution of trends in daily measurements of atmospheric ethane obtained from a weather station in the Swiss Alps, where the method can easily deal with the many missing observations due to adverse weather conditions.