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Pulsars show two classes of rotational irregularities that can be used tounderstand neutron-star interiors and magnetospheres: glitches and timingnoise. Here we present an analysis of the Vela pulsar spanning nearly 21 yr ofobservation and including 8 glitches. We identify the relative pulse number ofall of the observations between glitches, with the only pulse-numberambiguities existing over glitch events. We use the phase coherence of thetiming solution to simultaneously model the timing noise and glitches in aBayesian framework, allowing us to select preferred models for both. We findthe glitches can be described using only permanent and transient changes inspin frequency, i.e., no step changes in frequency derivative. For all of theglitches, we only need two exponentially decaying changes in spin frequency tomodel the transient components. In contrast to previous studies, we find thatthe dominant transient components decay on a common $\approx$ 1300 d timescale, and that a larger fraction ( $\gtrsim 25\%$) of glitch amplitudes areassociated with these transient components. We also detect shorter-durationtransient components of $\approx$ 25 d, as previously observed, but are limitedin sensitivity to events with shorter durations by the cadence of ourobservations. The timing noise is well described by a steep power-law processthat is independent of the glitches and subdominant to the glitch recovery. Thebraking index is constrained to be $<$ 8 with 95% confidence. This methodologycan be used to robustly measure the properties of glitches and timing noise inother pulsars.

Characterising the rotational irregularities of the Vela pulsar from 21 yr of phase-coherent timing