Suppose that $\{X_n\}_{n \geq 1}$ with $X_n \in \mathbb{R}^d$ is a random process (also can assume the process is Markov if that simplifies things). Does the following quantity have a specific name or interpretation?
$$V_N = \frac{1}{N} \sum_{n=1}^N X_n X_n^\intercal$$
I understand that if $X_n$ are i.i.d. then the above quantity is the empirical second moment and we have $V_N \rightarrow E[X_n X_n^\intercal]$. But what about the non i.i.d. case? For example, what is the interpretation of this quantity in a Gaussian random walk $X_n = X_{n-1} + \epsilon_{n-1}$, with $X_0 = 0, \epsilon_n \sim N(0,1)$?