Before revision:  The quantity of interest is defined as the integrated parameter over time T^{-1}\int_0^T\theta_t^*dt, where \theta_t^* is the time-varying parameter  .
After revision:  The quantity of interest is defined as the integrated parameter over time T^{-1}\int_0^T\theta_t^*dt, where \theta_t^* is the time-varying parameter , and we consider the high-frequency asymptotics .