Environmental Kuznets Curve depicts the long-term relationship between pollution and economic growth. It hypothesizes that during the initial stages of economic growth environmental quality will deteriorate, then, after reaching some turning point, it will improve as the economy grows. In the past decade, lots of empirical literature provided both supports and criticism to this hypothesis. However, as we know from econometrics, when data contain stochastic trends, the conclusions drawn from such analysis might be meaningless. In this paper, we test the stationarities of a number of key variables used in such analyses using a panel data set for 50 countries over 50 years. The tests with different null hypothesis find that the data are stochastically trending in the time-series dimension. Given this, the regressions and interpretation of pollution-growth models should be interpreted with care. Further tests on cointegration of appropriate model are required.