  In 1926, G. Udny Yule considered the following: given a sequence of pairs of
random variables $\{X_k,Y_k \}$ ($k=1,2, \ldots, n$), and letting $X_i = S_i$
and $Y_ i= S'_i$ where $S_i$ and $S'_i$ are the partial sums of two independent
random walks, what is the distribution of the empirical correlation coefficient
\begin{equation*} \rho_n = \frac{\sum_{i=1}^n S_i S^\prime_i -
\frac{1}{n}(\sum_{i=1}^n S_i)(\sum_{i=1}^n S^\prime_i)}{\sqrt{\sum_{i=1}^n
S^2_i - \frac{1}{n}(\sum_{i=1}^n S_i)^2}\sqrt{\sum_{i=1}^n (S^\prime_i)^2 -
\frac{1}{n}(\sum_{i=1}^n S^\prime_i)^2}}? \end{equation*} Yule empirically
observed the distribution of this statistic to be heavily dispersed and
frequently large in absolute value, leading him to call it "nonsense
correlation." This unexpected finding led to his formulation of two concrete
questions, each of which would remain open for more than ninety years: (i) Find
(analytically) the variance of $\rho_n$ as $n \rightarrow \infty$ and (ii):
Find (analytically) the higher order moments and the density of $\rho_n$ as $n
\rightarrow \infty$. In 2017, Ernst, Shepp, and Wyner considered the empirical
correlation coefficient \begin{equation*} \rho:= \frac{\int_0^1W_1(t)W_2(t) dt
- \int_0^1W_1(t) dt \int_0^1 W_2(t) dt}{\sqrt{\int_0^1 W^2_1(t) dt -
(\int_0^1W_1(t) dt)^2} \sqrt{\int_0^1 W^2_2(t) dt - (\int_0^1W_2(t)
dt)^2}}\end{equation*} of two independent Wiener processes $W_1,W_2$, the limit
to which $\rho_n$ converges weakly, as was first shown by Phillips (1986).
Using tools from integral equation theory, Ernst et al. (2017) closed question
(i) by explicitly calculating the second moment of $\rho$ to be .240522. This
paper begins where Ernst et al. (2017) leaves off. We succeed in closing
question (ii) by explicitly calculating all moments of $\rho$ (up to order 16).
