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We model the evolution of the magnetic fields of neutron stars as consistingof a long term power-law decay modulated by short term small amplitudeoscillations. Our model predictions on the timing noise $\ddot\nu$ of neutronstars agree well with the observed statistical properties and correlations ofnormal radio pulsars. Fitting the model predictions to the observed data, wefound that their initial parameter implies their initial surface magneticdipole magnetic field strength ~ 5E14 G at ~0.4 year old and that theoscillations have amplitude between E-8 to E-5 and period on the order ofyears. For individual pulsars our model can effectively reduce their timingresiduals, thus offering the potential of more sensitive detections ofgravitational waves with pulsar timing arrays. Finally our model can alsore-produce their observed correlation and oscillations of the second derivativeof spin frequency, as well as the "slow glitch" phenomenon.

Modeling pulsar time noise with long term power law decay modulated by short term oscillations of the magnetic fields of neutron stars