For example, this mentioned here: [link][1]. I also saw this in my data. I wonder - does anyone know a good reference where this is explained and justified more rigorously with some math and for some more-or-less wide class of processes?

Here are some plots:

Series with positive autocorrelation before differencing

![Series with positive autocorrelation before differencing][2]

Autocorrelation before differencing

![Autocorrelation before differencing][3]

Series after differencing

![Series after differencing][4]

Autocorrelation after differencing

![Autocorrelation after differencing][5]


  [1]: http://people.duke.edu/~rnau/411arim2.htm
  [2]: https://i.sstatic.net/TFOk3.gif
  [3]: https://i.sstatic.net/eRfd3.gif
  [4]: https://i.sstatic.net/lIctm.gif
  [5]: https://i.sstatic.net/EYj6j.gif