Zero offset corresponds to the middle line of the graph, as the utility I use is incapable of plotting negative values.
If you want to get started quickly, with the best results for minimum fuss, please see my Raspberry Pi NTP quick-starter page.
Please also see that page for issues with the Jessie release of Linux, and with the newer Raspberry Pi model 3.
heavy rain - it's possible that a layer of snow could attenuate the signal enough to stop the GPS receiving enough signal.
Monitoring performance may help you spot these problems.
(Thanks to Joe, HB9DRT for the information on snow - I've only seen that problem once here during an exceptionally cold winter).