  We report on a coherent timing analysis of the 163 Hz accreting millisecond
X-ray pulsar IGR J17062-6143. Using data collected with the Neutron Star
Interior Composition Explorer and XMM-Newton, we investigated the pulsar
evolution over a timespan of four years. We obtained a unique phase-coherent
timing solution for the stellar spin, finding the source to be spinning up at a
rate of $(3.77\pm0.09)\times 10^{-15}$ Hz/s. We further find that the $0.4-6$
keV pulse fraction varies gradually between 0.5% and 2.5% following a
sinusoidal oscillation with a $1210\pm40$ day period. Finally, we supplemented
this analysis with an archival Rossi X-ray Timing Explorer observation, and
obtained a phase coherent model for the binary orbit spanning 12 years,
yielding an orbital period derivative measurement of $(8.4\pm2.0) \times
10^{-12}$ s/s. This large orbital period derivative is inconsistent with a
binary evolution that is dominated by gravitational wave emission, and is
suggestive of highly non-conservative mass transfer in the binary system.
