Multirate time stepping is a numerical technique for efficiently solving large-scale ordinary differential equations (ODEs) with widely different time scales localized over the components. This technique enables one to use large time steps for slowly time-varying components, and small steps for rapidly varying ones. In this paper we describe a self-adjusting multirate time stepping strategy, in which the step size for a particular component is determined by its own local temporal variation, instead of using a single step size for the whole system. We primarily consider Rosenbrock methods, suitable for stiff or mildly stiff ODEs.