Long-term correlations in short, non-stationary time series: An application to international R&D collaborations

Within the perimeter of patent collaboration networks, the average distance of collaborations and the number of countries involved per each collaboration have been shown to have increased steadily in time. Less attention, though, has been devoted to assessing whether this growth of cross-country collaborations is stable in time. To address this scientific question we focus on the identification of long-term correlations (i.e. temporal persistence). Our data set consists of time series of yearly average collaboration radii and of cross-border links in the Euro-American subsystem of the global collaboration network for the period 1978-2014. To investigate the fundamental persistence properties of these time series, we use Detrended Fluctuation Analysis, a method that allows us to measure long-term correlations in detrended signals. Also, we devise a general and original procedure to assess the statistical significance of results for short time series. Our results, showing that long-term correlations do exist in the majority of our signals, reinforce the hypothesis of a diminishing role of geographical distance in technological collaborations. Results at national level show that a significant degree of heterogeneity in persistence parameters can be detected within Europe, irrespectively of the efforts towards the set-up of an integrated European Research Area.