interpreting a correlation plot (time series)

Hi, I've been asked to suggest a time series model based on the following correlation function, I was just wondering what you would suggest,

Yt 0.97 0.97 0.91 0.80 0.79
delta Yt -0.42 0.18 -0.02 0.07 -0.1

I can tell straight away that the time series Yt is non stationary, my problem is deciding whether the delta Yt correlations are indicative of exponential decay, or cutting off to 0 after a certain number of lags? Can anyone help me with identifying this?