相关系数=0即是独立的随机过程。

相关系数是衡量线性相关程度，只能说明不相关，无法说明独立。逆序检验和游程检验是检验独立的，但是缺陷又比较明显

indpependence assumption is more restrictive than zero correlation. indppendence implies martingale difference which further implies zero correlation. However, for the variance ratio test, zero corrlation is enough, becasue it suffices to show that the so-called "long run variance" is equal to "short run variance", i.e., dependence structure plays no role in the statistics. In fact, the variance of the partial sum of zero correlation process increase linearly which forms the basis of VR test.

不相关，说明就是独立。相关就说明不是独立事件。

你确定没有其他条件？