Stochastic trends in observed annual average temperature series

Annual average temperature series observed at individual stations and spatially averaged at continental, hemispheric, and global scales are analyzed in this study for the existence of deterministic and stochastic trends. In addition to using commonly-used statistical tests for the existence of deterministic and stochastic trends, verification of the existence of stochastic trends is strengthened by using near unit root autoregressive moving average (ARMA) models. It is shown that near unit root ARMA models fit all the observed temperature series where the statistical tests may suggest that stochastic trends do not exist but near unit root models suggest that they do exist. The combination of commonly-used statistical test results and near unit root ARMA model results obtained in this study further verify earlier findings that, in addition to deterministic trends, stochastic trends exist in the globally- and hemispherically-averaged annual average temperature series. Moreover, for the first time, it is demonstrated here that observed annual-average temperature series at many individual stations and averaged over five of the six continents also have stochastic trends; and globally-, hemispherically-, continentally-averaged temperature series and individual cities’ temperature series all share the same stochastic trend. Furthermore, it is revealed in this study that spatial averaging tends to make the stochastic trends more obvious and more easily detected.