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Time Series Analysis of Global Temperature Distributions: Identifying and Estimating Persistent Features in Temperature Anomalies

We analyze a time series of global temperature anomaly distributions to identify and estimate persistent features in climate change. In our study, temperature densities, obtained from globally distributed data over the period from 1850 to 2012, are regarded as a time series of functional observations that are changing over time. We employ a formal test for the existence of functional unit roots in the time series of these densities. Further, we develop a new test to distinguish functional unit roots from functional deterministic trends or explosive behavior. We find some persistent features in global temperature anomalies, which are attributed in particular to significant portions of mean and variance changes in their cross-sectional distributions. We detect persistence that is characteristic of a unit root process, but none of the persistence appears to be deterministic or explosive.