Why for a stationary time series the ACF will drop to zero relatively quickly? Stationarity is a form of dependence and the ACF (and the PACF) measure the dependence between two r.v's, it's seems a contradiction to me (of course I'm wrong, but I don't understand why).
We can use Ljung-box test to test stationarity. Stationarity is a form of dependence. If the series is stationary I'll refuse the null hypothesis, that is independence. Is it correct?