Difference between stationarity and ergodicity I am currently studying time series. However, I have trouble understanding how ergodicity and stationarity differ.
Could someone clarify the difference between the two concepts in simple terms and maybe give an example?

A very simple example of a series which is stationary but not ergodic is the following:
$$ X_t = \sin(2\pi t + \Omega), \quad t=0,2,3,\dotsc  $$
where $\Omega \sim \mathcal{Unif}(0, 2\pi)$. Observe that by the periodicity of $\sin$ we have
$$ X_0=\sin(\Omega), X_1=\sin(\Omega), X_2=\sin(\Omega), \dotsc  $$ so the time mean is $\sin(\Omega)$, a random variable, different from the ensemble mean of $0$.
