Olivia Kvist | Searcharxiv

arXiv2026

Cointegration by Parts: Locating Cointegration in Time

Tests for cointegration are typically applied to a single window spanning the entire sample, assuming that the long-run relationship holds throughout. When it holds over only a part of the sample, such tests lose power, because the stationary episode is diluted by periods without cointegration. We propose three statistics for testing whether two or more series cointegrate only over a part of the sample, each an infimum of the Engle-Granger statistic over recursive, backward-expanding, or doubly-flexible windows. We derive their limiting distributions and establish which alternatives each is consistent against. Only the doubly-flexible statistic has power against both break directions. Inspired by the seminal work of James G. MacKinnon, critical values are obtained by simulation and summarized through response surface regressions. We apply the tests to global mean sea level and global mean surface temperature anomalies. All three reject the null of no cointegration at the 5% level, locating it in a sub-period of the 1880--2019 record that coincides with documented discontinuities in sea surface temperature data collection.

stat.ME↗

arXiv2024

Breaching 1.5°C: Give me the odds

Climate change communication is crucial to raising awareness and motivating action. In the context of breaching the limits set out by the Paris Agreement, we argue that climate scientists should move away from point estimates and towards reporting probabilities. Reporting probabilities will provide policymakers with a range of possible outcomes and will allow them to make informed timely decisions. To achieve this goal, we propose a method to calculate the probability of breaching the limits set out by the Paris Agreement. The method can be summarized as predicting future temperatures under different scenarios and calculating the number of possible outcomes that breach the limits as a proportion of the total number of outcomes. The probabilities can be computed for different time horizons and can be updated as new data become available. As an illustration, we performed a simulation study to investigate the probability of breaching the limits in a statistical model. Our results show that the probability of breaching the 1.5°C limit is already greater than zero for 2024. Moreover, the probability of breaching the limit is greater than 99% by 2042 if no action is taken to reduce greenhouse gas emissions. Our methodology is simple to implement and can easily be extended to more complex models of the climate system. We encourage climate model developers to include the probabilities of breaching the limits in their reports.

stat.AP↗