Mining massive daily news media data to infer patterns of cultural trends, including political conflicts and instabilities, is an important goal of computational social science and the new interdisciplinary field called "culturnomics." While the sheer size of media data makes this task challenging, a greater hurdle is the nonstationarity of data, manifested in several ways, which invalidates surge in media coverage as a reliable indicator of political change. We demonstrate the use of advanced statistical, information-theoretic, and random fractal methods to analyze CAMEO-encoded political events data. In particular, we show that on the country level, event distributions obey a Zipf-Mandelbrot law, and interactions among countries follow an exponential law, indicating that local or prioritized events dominate the political environment of a country. Most importantly, we find that world-wide political instabilities, such as the Arab Spring, are associated with breakdown or enhancement of long-range correlations in political events.