Abstract:

This talk focuses on independent testing of two stochastic processes. In contrast to i.i.d. random variable data, data originating from a stochastic process typically exhibit strong correlations. This inherent feature of stochastic processes poses significant challenges when conducting statistical inference. In this talk, we will commence by reviewing the historical context of Yule's nonsense correlation. This correlation is defined as the correlation of two independent random walks whose distribution is known to be heavily dispersed and frequently large in absolute value. This phenomenon demonstrates the difficulty inherent in conducting statistical inference for stochastic processes. The second part of the talk is devoted to AR(1) processes. We investigated the convergence rate of the distribution of the correlation between two independent AR(1) processes to the normal distribution. Our analysis demonstrates that this convergence rate follows the order of the square root of the fraction logarithm of n over n, with n representing the length of the processes. Finally, we will discuss the potential for a new methodology to test the independence of both random walks and AR(1) processes.