Suppose $X_n$ is a WSS Gaussian stochastic process with(every subsample of the process is jointly gaussian):
- $E[X_n]=\mu$ for all n
- $R_{xx}[l] $ is the autocorrelation function
I wish to calculate : $E[X_{n_1}\cdot X_{n_2} \cdot X_{n_3}]$ for $n_1 \neq n_2 \neq n_3$.
Would this be the same as calculating the third moment of a single gaussian R.V distributed as $N(\mu,R_{xx}[0] )$ ? (which is $\mu^3+ 3\sigma^2\mu,$ where $\sigma^2 = R_{xx}[0]$)
If so, why?