In a way, gravitational waves are "waves of time". Or maybe it would be better to say "waves of time dilation". Take a look at this physicsworld report on today's LIGO announcement:
"The LIGO facility does not, however, measure the change in path-length because the gravitational wave compresses or expands the light's wavelength too. Instead, what the device reveals are tiny shifts in the period of the two light beams. If the crests or troughs of the wave arrive out of synch, they produce an interference pattern, meaning that the light acts as a clock and not a ruler".
Hence in the LIGO paper on page 3 they say "passing gravitational wave effectively alters the arm lengths". Note the word effectively.