In this talk, under discrete observations, we study the Cramer-type moderate deviations of Yule's nonsense correlation statistic for two Ornstein-Uhlenbeck processes.  As applications, the global and local powers of the hypothesis testing for the independence between two Ornstein-Uhlenbeck processes are shown to approach one exponentially. The main methods consist of the deviation inequalities and Cramer-type moderate deviations for multiple Wiener-Ito integrals and asymptotic analysis techniques.