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

Constraints on the massive graviton dark matter from pulsar timing and precision astrometry