Let's say we have samples of a random process $X(t)$ at two different times, $t_1$ and $t_2$, denoted $X(t_1), X(t_2)$. The values of $X(t)$ represent some voltage-like quantity (i.e. a voltage, current, or field). Assume $X(t)$ is a zero-mean, real-valued wide-sense stationary (WSS) process.
For the second-order statistics, we usually treat the quantity $\mathbb E[X^2(t)]$ as the average power.
The expectation $\mathbb E[X(t_1) X(t_2)]$ is just the autocorrelation function evaluated at lag $\tau = t_2-t_1$.
Is there some physical interpretation of the 4th-order correlations, i.e. $\mathbb E[X^3 (t_1)X(t_2)]$, $\mathbb E[X^2 (t_1)X^2(t_2)]$, and $\mathbb E[X (t_1) X^3(t_2)]$?