A statistical analysis of time trends in atmospheric ethane

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. As with 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 (we provide R code for all proposed methods on https://www.stephansmeekes.nl/code.).

Stratospheric Fluorine as a Tracer of Circulation Changes: Comparison Between Infrared Remote‐Sensing Observations and Simulations With Five Modern Reanalyses

“…Since the {   t E } are not independent anymore, this ARW bootstrap method will capture some of the autocorrelation of the time series while preserving its heteroskedasticity. The choice of γ constitutes a trade-off between allowing for variation in the bootstrap samples (small γ values, falling back to the wild bootstrap) and capturing more autocorrelation (   1 E ; Friedrich, Beutner, et al, 2020). The parameter γ can either be chosen (thus acting as a tuning parameter) or determined as a function of the sample size n. We follow the latter case and, as suggested by Smeekes and Urbain (2014), Friedrich, Beutner, et al (2020),…”

Trend detection of atmospheric time series

“…Bootstrap is a resampling procedure that can be used for estimating the sampling distribution about the trends and/or their uncertainty. This technique is also known for its ability to mitigate the violation of normality assumption and for being robust to autocorrelation and heteroskedasticity in the errors (Politis and White, 2004;Gardiner et al, 2008;Noguchi et al, 2011;Friedrich et al, 2020aFriedrich et al, , 2020b. Bootstrap-based approaches are commonly adopted by practitioners due to their simplicity.…”

“…Therefore, one should not use simple curve fitting techniques, such as polynomials, to perform change point analysis. Instead, a formal test of appropriateness and meaningfulness of change point is preferred (Friedrich et al, 2020a).…”

“…A further important aspect for atmospheric composition trends is the detection and/or quantification of trend changes. This is especially relevant in the policy arena to determine the efficacy of certain air quality measures (Box and Tiao, 1975) or to examine whether the changes can be attributable to other natural or human-caused factors (Reinsel et al, 2005;Friedrich et al, 2020a).…”

Essays on nonstationary nonlinear time series models

“…Practitioners often make use of a linear time trend to describe the long-term, smooth tendencies that appear in levels of data. It is not surprising that evidence of structural changes in deterministic trends is widely found in different disciplines such as macroeconomics and climatology, see, e.g., Perron (1989), Raj and Slottje (1994), Estrada and Perron (2017) and Friedrich et al (2020).…”