As b*cat has said, any load switching device such as a heating/zone thermostat can generate noise either directly or via mains wiring, had an occurance on my daughters system where the oil fired boiler thermostat was generating a considerable amount of noise clearly visable on the router stat's and also causing a "stutter" on all the house terrestrial TV's running on an amplified distribution system from outside aerials.
In this case I believe the interference was transmitted through the mains certainly in the case of the house TV's, not so sure about the interaction with the modem/router.
Anyway, replacement of the boiler stat. completely cured the issue on TV's and modem/router.
Likely stating the obvious, but it's all down to a process of elimination, being able to identify/eliminate if possible any local events which correspond to the modem/router recorded disturbances as logged by DSLStats.
Initial quick checks can be carried out on the heating/zone stats. by adjusting their respective set points loading and unloading, however, this is not completely fool proof as set point adjustment can be quick and "clean" whereas normal temperature change which is usually a much slower action can produce contact "noise" when approaching the set point from either direction, the classic symptoms of a dodgy thermostat.
Then, as g3uiss has said, after all local sources of interference have been eliminated it's down to possible external sources which is a completely different ball game.