  Stochastic temporal wandering of the spin frequency $\nu$ of a
rotation-powered pulsar (i.e.~the achromatic component of timing noise
unrelated to interstellar propagation) affects the accuracy with which the
secular braking torque can be measured. Observational studies confirm that
pulsars with anomalous braking indices $\vert n \vert = \vert \nu \ddot{\nu} /
\dot{\nu}^2 \vert \gg 1$ exhibit elevated levels of timing noise, where an
overdot symbolizes a derivative with respect to time. Here it is shown, through
analytic calculations and Monte Carlo simulations involving synthetic data and
modern Bayesian timing techniques, that the variance $\langle n^2 \rangle$ of
the measured $n$ scales with the square of the timing noise amplitude
$\sigma_{\ddot{\nu}}$. The anomalous regime $\langle n^2 \rangle \gg 1$
corresponds to $ \sigma_{\ddot{\nu}}^2 \gg 10^{-60}
(\gamma_{\ddot{\nu}}/10^{-6} \, {\rm s^{-1}})^2 (\dot{\nu} / 10^{-14} \, {\rm
Hz \, s^{-1}})^4 (\nu / 1 \, {\rm Hz})^{-2} (T_{\rm obs} / 10^8 \, {\rm s}) \,
{\rm Hz}^2{\rm s}^{-5 }$, where $\gamma_{\ddot{\nu}}$ is a stellar damping
time-scale, and $T_{\rm obs}$ is the total observing time. When the inequality
in the above condition is reversed, $n$ is dominated by the secular braking
torque, and timing measurements return $n\sim 3$, if the secular braking torque
is electromagnetic. The variance $\langle n^2 \rangle$ is greater, when the
stochastic process driving spin fluctuations differs from the red noise model
(e.g. power-law spectral density) assumed in the timing solution.
