What to read from the autocorrelation function of a time series? Given a time series, one can estimate the autocorrelation-function and plot it, for example as seen below:


What is it then possible to read about the time series, from this autocorrelation-function? Is it for example possible to reason about the stationarity of the time series?
Edited: Here I have included the ACF of the differenced series with more lags

 A: this acf suggests non-stationarity which might be remedied by incorporating a daily effect as it appears to evidence structure at lag 24. The daily effect could be either auto-regressive of order 24 or it might be deterministic where 23 hourly dummies might be needed. You could try either of these and assess the results. Further structure appears to be needed. This could be either the need to include level shifts or some form of short-term auto-regressive structure like a differncing operator of lag 1. After identifying and estimating a useful mode, the residuals might suggest further action (model augmentation)to ensure that the signal has fully extracted all information and rendered a noise process that is normal or Gaussian. This will then answer your vague question regarding "stability". Hope this helps !
A slight addition !
The word "suggests" is used as the acf is not the final word on this while the actual data is. In the absence of the actual data the acf is sometimes useful in characterizing the process.
