The empirical correlations are fairly strong as shown by
both Dickey et al and Wyatt & Curry, but I don't consider that strong evidence as the correlation consists really only of very few minimums and maximums.
So we're back to exchanging angular momentum between the lithosphere (crust + solid mantle) and the core, mediated somehow by the asthenosphere, the same picture as in
Dickey et al 2011 and its many predecessors: «Previous investigators have found that the LOD fluctuations are largely attributed to core - mantle interactions.»
Variations in the speed of the earth's spin in the form of length of day may fire the imaginations of curve - fitters with graphs like this from
Dickey et al (2011) matching Length of Day against global temperature shorn of AGW.