# A statistical analysis of time trends in atmospheric ethane

## TL;DR

This paper develops advanced statistical methods to analyze long-term atmospheric ethane data, addressing autocorrelation, heteroskedasticity, seasonality, and missing data to identify meaningful trends and trend reversals.

## Contribution

It introduces bootstrap-based techniques for detecting trend changes and estimating their timing in complex atmospheric time series with multiple data challenges.

## Key findings

- Effective detection of trend reversals in ethane levels.
- Robust confidence bands for nonlinear trend estimation.
- Method handles autocorrelation, heteroskedasticity, seasonality, and missing data.

## Abstract

Ethane is the most abundant non-methane hydrocarbon in the Earth's atmosphere and an important precursor of tropospheric ozone through various chemical pathways. Ethane is also an indirect greenhouse gas (global warming potential), influencing the atmospheric lifetime of methane through the consumption of the hydroxyl radical (OH). Understanding the development of trends and identifying trend reversals in atmospheric ethane is therefore crucial. Our dataset consists of four series of daily ethane columns obtained from ground-based FTIR measurements. As many other decadal time series, our data are characterized by autocorrelation, heteroskedasticity, and seasonal effects. Additionally, missing observations due to instrument failure or unfavorable measurement conditions are common in such series. The goal of this paper is therefore to analyze trends in atmospheric ethane with statistical tools that correctly address these data features. We present selected methods designed for the analysis of time trends and trend reversals. We consider bootstrap inference on broken linear trends and smoothly varying nonlinear trends. In particular, for the broken trend model, we propose a bootstrap method for inference on the break location and the corresponding changes in slope. For the smooth trend model we construct simultaneous confidence bands around the nonparametrically estimated trend. Our autoregressive wild bootstrap approach, combined with a seasonal filter, is able to handle all issues mentioned above.