Interesting study. There are several timescales involved in LOD changes.
The shortest time-scale is directly related to diurnal and semidiurnal lunisolar tides. This one also impacts earthquakes as per the recent USGS and Japan research
The intermediate time-scale is empirically related to ENSO, but I think this transitively relates to lunar forcing, which is discussed over on the ENSO threads. In other words, lunar forces ENSO, which then contributes to the LOD changes.
The longest time-scale is most puzzling to me, as the change is so gradual, but is thought to be due to mantle changes:
Here they are on Chao's chart:
That long one is the focus of the program