Vol. 124, No. 3 * Pages 311–426 * July - September 2020

Temperature changes are in the focus of climate research. There are many analyses available, but they rarely apply rigorous mathematics for assessing the results.
The main approach of this paper is the dependent weighted bootstrap. It is a simulation method, where both the fitted regression and the dependency among the data are taken into account. We present a simulation study showing that for serially dependent data it is the most accurate in case of estimating the coefficient in a linear regression.
This paper shows an analysis of the gridded European temperature data. We have used the 0.5° × 0.5° grid of daily temperatures for 68 years (from 1950 to 2017), created by the European Climate Assessment. We investigated the speed of the global warming by changing the starting point of the linear regression. The significance of the differences between the coefficients was tested by the dependent weighted bootstrap. We have shown that the acceleration was significant for large regions of Europe, especially the central, northern and western parts.
The vast amount of results is summarized by a Gaussian model-based clustering, which is the suitable approach if we intend to have clusters that are spatially compact. The number of clusters was chosen as 13, by a suitably modified "elbow rule". This approach allows to compare the speed and acceleration of warming for different regions. The quickest warming in the last 40 years was observed in Central and Southwestern Europe, but the acceleration is more pronounced in Central Europe.