Precision pulsar timing provides a powerful tool to probe pulsar emission, interstellar mediums, gravitational theories and low-frequency gravitational waves. An important issue in the pulsar timing is the rotational stability, which lays the foundation of precision timing. Spatial motions such as radial velocity affects the apparent pulsar rotation by contributing to a frequency second derivative to the pulsar spin. This kinematic effect was analysed in previous studies by assuming none-correlated timing noise, which is problematic in most cases. In this talk, I will focus on the correlated timing noise and discuss its impacts on constraining the frequency second derivative. Using the new constrains on this spin parameter, I will talk about applications to study the millisecond pulsars in the pulsar timing array.