tokens: pulsars. Timing noise manifests as a red-noise (time-correlated) process in the TOAs, and is typically described by a wide-sense stationary stochastic process (Groth 1975 ), modelled as either random walks in the pulsar spin parameters, or with a more general power spectrum. The origin of this noise is unclear. While some of it may be caused by variable torques associated with changes in the pulsar magnetosphere state (Lyne et al. 2010 ), a significant fraction is likely associated with rotational irregularities interior to the star (Melatos Link 2014 ). The properties of timing noise vary markedly across the pulsar population, with its strength depending on the pulsar spin frequency ν and frequency derivative (Shannon Cordes 2010 ), and likely other factors because of the large dispersion levels of timing noise between pulsars. For example, the most stable MSP, PSR J1909−3744 shows no evidence for instabilities with phase variations limited ≲100 ns (≈0.3 per cent of pulse phase) over 11 yr (Shannon et al. 2015 ). In contrast, the timing noise in young pulsars and magnetars can contribute many cycles of pulse phase on week to month time-scales (Livingstone et al. 2011 ), both making it difficult to find a phase-coherent solutions in poorly sampled data and presenting challenges to TOA-modelling algorithms. While finding the origin of timing noise is important for understanding neutron stars, it is also necessary to account for timing noise as part of a general timing model for the pulsar. This is necessary to eliminate, or at least mitigate, bias in the estimation of other parameters in the model (Coles et al. 2011 ; van Haasteren Levin 2013 ; Lentati et al. 2014 ; Kerr et al. 2015 ). In addition to exhibiting timing noise, pulsars can experience glitch events (e.g. Espinoza et al. 2011 ; Yu et al. 2013 ), in which they are observed to suddenly change spin state, with the most significant component being increases in spin frequency that can exceed 1: 10 5 (Manchester Hobbs 2011 ). Glitches have been modelled with permanent changes in ν and , as well as transient components, in which changes in ν are modelled to decay (typically exponentially) on time-scales τ. Occasionally multiple glitch-decay components (with different time-scales) are invoked, particularly when high cadence (daily or higher) observations (e.g. Dodson, McCulloch Lewis 2002 ). Glitch components are often identified and characterized by searching for variation of spin frequency and frequency derivative in subsets of the data (Lyne et al. 2015 ). This method is suboptimal because it does not utilize the phase coherence of the pulse arrival times. The study of glitches is further complicated by the presence of timing noise. There are two prevailing theoretical models for glitches. In the first, glitches are associated with the transfer of angular momentum between the superfluid interior and solid crust of the neutron star (Anderson Itoh 1975 ; Alpar et al. 1984 ). A
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