This paper examines local changes in annual temperature data for the northern and southern hemispheres (1850–2017) by using a multivariate generalization of the shifting-meanautoregressive model of González and Teräsvirta (2008). Univariate models are first fitted to each series by using the QuickShift methodology. Full information maximum likelihood estimates of a bivariate system of temperature equations are then obtained and asymptotic properties of the corresponding estimators considered. The system is then used to perform formal tests of co-movements, called co-shifting, in the series. The results show evidence of co-shifting in the two series.