# ARMA and differencing time series, Theory questions

True/False Statements, if false make them true:

1.The model Yt = Yt-1 + ut, where ut is a white noise process, is a process whose logarithm is stationary.

My idea: So the model itself is not stationary since its a random walk, but if i take the logarithm that should change right?

2. The model Yt = Yt-1+δ+ ut , where ut is a stationary ARMA(1,1) process with E(ut)=0, models a time series where the growth rates ∇Yt are uncorrelated

No idea if the second one is true.

1. I assume you mean second order stationary. If $Y_t$ is not second order stationary, it is because the mean and/or variance change overtime. If that be the case, I see no way the mean and/or variance of $\log(Y_t)$ could remain the same.
2. Growth rates as you define them are $\delta + u_t$. Take the particular case $\delta=0$ to make things simpler: that leaves you with $u_t$ which, being ARMA(1,1), is not an uncorrelated process.