  In the standard two-component crust-superfluid model of a neutron star,
timing noise can arise when the two components are perturbed by stochastic
torques. Here it is demonstrated how to analyse fluctuations in radio pulse
times of arrival with a Kalman filter to measure physical properties of the
two-component model, including the crust-superfluid coupling time-scale and the
variances of the crust and superfluid torques. The analysis technique,
validated previously on synthetic data, is applied to observations with the
Molonglo Observatory Synthesis Telescope of the representative pulsar PSR
J1359$-$6038. It is shown that the two-component model is preferred to a
one-component model, with log Bayes factor $6.81 \pm 0.02$. The coupling
time-scale and the torque variances on the crust and superfluid are measured
with $90\%$ confidence to be $10^{7.1^{+0.8}_{-0.5}}$ $\rm{s}$ and
$10^{-24.0^{+0.4}_{-5.6}}$ $\rm{rad^2~s^{-3}}$ and $10^{-21.7^{+3.5}_{-0.9}}$
$\rm{rad^2~s^{-3}}$ respectively.
