So the question asks whether this is a stationary time series: (i) Xt = sin(wt + U), where U is uniformly distributed on [0,2pi] The solution says that because it is not purely indeterministic, it is not a stationary time series. What I don't understand is why? The definition given for a purely indeterministic process is that "knowledge of values of X1,...Xn is progressively less useful at predicting the value or XN as N->inf. " I take this to mean that you can't use say, the value of X1 to predict the value of X10. But if we have a uniform distribution then we can predict the value of X10 because... it's uniform? (That's the best I can come up with).
I think the issue is that because it is cyclical you will always know roughly where it is in the future (plus a little random variation due to the uniform distribution) and so the connection between the values does not decrease over time...
