A
ActSciStudent9
Member
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) 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).
