The purpose of this article is to provide an exact formula for the second moment of the empirical correlation of two independent Gaussian random walks, as well as implicit formulas for higher moments. The proofs are based on a symbolically tractable integro-differential representation formula for the moments of any order in a class of empirical correlations, first established by \cite{ernst2019distribution} and investigated previously in \cite{ernst2017yule}.

翻译：本条的目的是为两个独立的高山随机行走的经验相关性的第二个时刻以及更高时刻的隐含公式提供一个精确的公式。 证据基于在某类经验相关性中任何时刻的象征性可移动的异种分布式代表公式, 最初由\ cite{ ernst2019 sission} 确定, 先前在\ cite{ ernst2017yule} 中调查过 。