What you're looking for is a test for homoskedasticity. I haven't need to use this myself yet, so I can't offer much in-depth advice, but the wikipedia page on homoskedasticity lists a couple of tests, including the Breusch–Pagan test, which assumes normality in the data, the Koenker–Basset test which generalises the Breusch–Pagan test for non-normal data.
bptest function in the
lmtest R package implements the both tests (set
studentize=true for the Koenker–Basset test). Looks like it's only for linear models though, so it might not work for your data.
There's a few interesting questions about these test on this site. Check out charlie's answer on Why does the Breusch-Pagan test fail? in particular.