The inter-glitch timing of the Vela pulsar is characterized by a constant second derivative of the rotation rate .
This takes over after the post-glitch exponential relaxation , and is completed at about the time of the next glitch .
The vortex creep model explains the second derivatives in terms of non-linear response to the glitch .
We present inter-glitch timing fits to the present sample covering 16 large glitches , taking into account the possibility that in some glitches part of the step in spin-down rate may involve a “ persistent shift ” , as observed in the Crab pulsar .
Modifying the expression for the time between glitches with this hypothesis leads to better agreement with the observed inter-glitch time intervals .
We extrapolate the inter-glitch model fits to obtain spin-down rates just prior to each glitch , and use these to calculate the braking index n = 2.81 \pm 0.12 .
The next glitch should occur around Dec. 22 , 2017 \pm 197 days if no persistent shift is involved , but could occur as early as July 27 , 2016 \pm 152 days if the 2013 glitch gave rise to a typical Vela persistent shift . Note added : Literally while we were submitting the first version of this paper , on Dec. 12 , 2016 , we saw ATel \# 9847 announcing a Vela pulsar glitch which has arrived 138 days after our prediction with a persistent shift , within the 1 \sigma uncertainty of 152 days .