What is the difference between a time series without autocorrelation, and a stationary time series?
If they are the same, why do we need to do both the Ljung-Box test and unit root test?
Consider a time series where the value at epoc $\displaystyle i$ is normally distributed with zero mean and variance $\displaystyle \sigma_i^2=|i|$ and independedent of the values at all other epocs. The autocorrelation of this process is clearly zero for all non-zero lags and it is also clearly non-stationary.
CB