Hi all,A question about Stationarity.If Y(t) = G(t) + F where G is distributed as (independent) Uniform [0,1] and F is distributed as (independent) N(0,1) with E[G(t)F] =0 the process is stationary but not ergodic.If Y(t) = G(t) + F(t) where G is distributed as (independent) Uniform [0,1] and F is distributed as (independent) N(0,1) with E[G(t)F] =0 is this process ergodic?Thank you in advance

I don't understand your question. "Stationary" and "ergodic" depend on the definition of the time series. You have given a formula for a particular time value, Y(t), but no clue how this relates to Y(x) for any other time. You don't tell us whether the definition of Y(t) is unconditional or conditional. The only difference between your two formulations is F becomes F(t). That seems to say that in the first series, a random number F is chosen from a Normal distribution and added to Y for all t. In that case the distribution it came from is irrelevant to the time series properties of Y, it is just a constant. If you tell us how the time series is formed, we can help you determine if it is stationary or ergodic.

The idea is the following:(for the first process)ensemble average E[Yt]=E[Gt]+E[F] = 0.5 + 0time average y(super bar) = 1/n *( the Sum of G) + F = so the time average is equal to 0.5 + F. F is equal to 0 with probability 0 so the time average and the ensamble average are not the same and the process is not ergodic. In other words F is not averaged out from the time average like it is from the esemble average.Is in your opinion correct this argument?Thank you

It still doesn't make sense to me. Where does t come in? How does Y(t1) relate to Y(t2)?

ergody is definitions of another stationary of process (data generation processes just like time series) ??