  We test models for the evolution of neutron star (NS) magnetic fields (B).
Our model for the evolution of the NS spin is taken from an analysis of pulsar
timing noise presented by Hobbs et al. (2010). We first test the standard model
of a pulsar's magnetosphere in which B does not change with time and magnetic
dipole radiation is assumed to dominate the pulsar's spin-down. We find this
model fails to predict both the magnitudes and signs of the second derivatives
of the spin frequencies ($\ddot{\nu}$). We then construct a phenomenological
model of the evolution of $B$, which contains a long term decay (LTD) modulated
by short term oscillations (STO); a pulsar's spin is thus modified by its
B-evolution. We find that an exponential LTD is not favored by the observed
statistical properties of $\ddot{\nu}$ for young pulsars and fails to explain
the fact that $\ddot{\nu}$ is negative for roughly half of the old pulsars. A
simple power-law LTD can explain all the observed statistical properties of
$\ddot{\nu}$. Finally we discuss some physical implications of our results to
models of the B-decay of NSs and suggest reliable determination of the true
ages of many young NSs is needed, in order to constrain further the physical
mechanisms of their B-decay. Our model can be further tested with the measured
evolutions of $\dot{\nu}$ and $\ddot{\nu}$ for an individual pulsar; the decay
index, oscillation amplitude and period can also be determined this way for the
pulsar.
