Does the sequence $\{x _{t}\}_{t=1}^{n}$ satisfy the following conditions if it is generated from a normal distribution with a mean of 0 and a standard deviation of 3?
*Stationary? Yes, because the sequence's first and second moments are finite.
*Martingale difference sequence? Yes, because the time series' expectation is zero.
*Ergodic process?
My question is how do I demonstrate that the sequence is ergodic?