Cointegration is a property of N-dimensional time series, which says that each individual component is non -stationary (growing like a random walk), but there exists a stationary linear combination. Testing procedures for the presence of cointegration has been extensively studied in statistics and economics, but most results are restricted to the case when N is much smaller than the length of the time series. I will discuss the recently discovered mathematical structures, which make the large N case accessible. On the applied side we will see a remarkable match between predictions of random matrix theory and behavior of S&P 100 stocks. On the theoretical side we will see how ideas from statistical mechanics and asymptotic representation theory play a crucial role in the analysis. (Based on joint work with Anna Bykhovskaya.)