Hi, a probabilistic question here. Consider zero mean random variables $X_1,\dots,X_N$ with unknown distributions. Actually they have random distributions such that the covariance between $X_i$ and $X_j$ is determined by some discrete random variable $Z_{ij}$. Then $E[X_iX_j]$ averages over $Z_{ij}$, while $E[X_iX_j|Z_{ij}]$ gives the "true" covariance in a sense that I use fixed distributions for $X_i$ and $X_j$ rather than random ones.
Analogy to stationary zero mean times series: $E[X_tX_s]=r(|t-s|)$ for some known function $r$. The difference in my case is that this lag $|t-s|$ correspo…