Frequency-Domain Evidence for Climate Change

Abstract

The goal of this paper is to search for conclusive evidence against the stationarity of the global air surface temperature, which is one of the most important indicators of climate change. For this purpose, possible long-range dependencies are investigated in the frequency-domain. Since conventional tests of hypotheses about the memory parameter, which measures the degree of long-range dependence, are typically based on asymptotic arguments and are therefore of limited practical value in case of small or medium sample sizes, we employ a new small-sample test as well as a related estimator for the memory parameter. To safeguard against false positive findings, simulation studies are carried out to examine the suitability of the employed methods and hemispheric datasets are used to check the robustness of the empirical findings against low-frequency natural variability caused by oceanic cycles. Overall, our frequency-domain analysis provides strong evidence of non-stationarity, which is consistent with previous results obtained in the time domain with models allowing for stochastic or deterministic trends.

Temperature Anomalies, Long Memory, and Aggregation

“…Finally, note that the results from Table 5 are in line with the ones from Mangat and Reschenhofer (2020). The authors use some of the semiparametric estimators considered in this study along with the small-sample estimator developed by Reschenhofer and Mangat (2020).…”

“…The authors noted that long memory should be incorporated in trend estimations for temperature series to obtain correct confidence intervals. More recently, Baillie and Chung (2002) and Mills (2007) use fractionally differenced models to estimate the long memory parameter, while Gil-Alana (2005) and Mangat and Reschenhofer (2020) use semiparametric estimators in the frequency domain. They all conclude that temperature data possess long memory.…”