Abstract 

  Red noise is widespread in the timing residuals of radio pulsar timing, but still poorly understood so far. In a series of papers, we have developed a model on the red noise of radio pulsar timing, which can explain the statistical properties and the patterns in the timing residuals of radio pulsars. Applying our model to the existing data reveals the long term decay of the magnetic fields of pulsars and the oscillation of the inclination angle of their magnetic axes. This model may also be used to improve the sensitivity and precision of detecting gravitational waves and space navigation using pulsars.