Almost all earthquakes at Yellowstone are brittle-failure events caused when rocks break due to crustal stresses. Though we've been looking at Yellowstone for years, no one has yet identified "long-period (LP) events" commonly attributed to magma movement. If LP events are observed, that will NOT mean Yellowstone is getting ready to erupt. LP earthquakes commonly occur at other volcanoes in the world, including volcanoes in California, that have not erupted for centuries or millennia. One variety of ground shaking called “tremor” is observed at Yellowstone's geothermal areas whenever water boils in a geyser.
The largest historic earthquake in the Rocky Mountains was a magnitude 7.3 earthquake at Hebgen Lake northwest of Yellowstone in 1959. It was caused by the extension--or stretching--of the Earth's crust. The earthquake displaced a 40-km-long fault (25 miles) that rose vertically up to 12 meters (40 feet).
Shaking from earthquakes can also change the way that Yellowstone's hydrothermal system behaves. The interval between eruptions of Old Faithful Geyser increased significantly following the 1959 earthquake.