  The effect of a narrow-band isotropic stochastic GW background on pulsar
timing and astrometric measurements is studied. Such a background appears in
some theories of gravity. We show that the existing millisecond pulsar timing
accuracy ($\sim 0.2 \rm{\mu s}$) strongly constrains possible observational
consequences of theory of massive gravity with spontaneous Lorentz braking
\cite{dtt:2005}, essentially ruling out significant contribution of massive
gravitons to the local dark halo density. The present-day accuracy of
astrometrical measurements ($\sim 100 \rm{\mu as}$) sets less stringent
constraints on this theory.
