  Pulsars are known to display short-term variability. Recently, examples of
longer-term emission variability have emerged that are often correlated with
changes in the rotational properties of the pulsar. To further illuminate this
relationship, we have developed techniques to identify emission and rotation
variability in pulsar data, and determine correlations between the two.
Individual observations may be too noisy to identify subtle changes in the
pulse profile. We use Gaussian process (GP) regression to model noisy
observations and produce a continuous map of pulse profile variability.
Generally, multiple observing epochs are required to obtain the pulsar spin
frequency derivative ($\dot{\nu}$). GP regression is, therefore, also used to
obtain $\dot{\nu}$, under the hypothesis that pulsar timing noise is primarily
caused by unmodelled changes in $\dot{\nu}$. Our techniques distinguish between
two types of variability: changes in the total flux density versus changes in
the pulse shape. We have applied these techniques to 168 pulsars observed by
the Parkes radio telescope, and see that although variations in flux density
are ubiquitous, substantial changes in the shape of the pulse profile are rare.
We reproduce previously published results and present examples of profile shape
changing in seven pulsars; in particular, a clear new example of correlated
changes in profile shape and rotation is found in PSR~J1602$-$5100. In the
shape changing pulsars, a more complex picture than the previously proposed two
state model emerges. We conclude that our simple assumption that all timing
noise can be interpreted as $\dot{\nu}$ variability is insufficient to explain
our dataset.
