  We present an anisotropic analysis of Baryon Acoustic Oscillation (BAO)
signal from the SDSS-IV extended Baryon Oscillation Spectroscopic Survey
(eBOSS) Data Release 14 (DR14) quasar sample. The sample consists of 147,000
quasars distributed over a redshift range of $0.8 < z < 2.2$. We apply the
redshift weights technique to the clustering of quasars in this sample and
achieve a 4.6 per cent measurement of the angular distance measurement $D_M$ at
$z = 2.2$ and Hubble parameter $H$ at $z=0.8$. We parameterize the
distance-redshift relation, relative to a fiducial model, as a quadratic
expansion. The coefficients of this expansion are used to reconstruct the
distance-redshift relation and obtain distance and Hubble parameter
measurements at all redshifts within the redshift range of the sample.
Reporting the result at two characteristic redshifts, we determine $D_M(z=1) =
3405\pm305 \ (r_{\rm d} / r_{\rm d, fid}) \ {\rm Mpc}$, $H(z=1) = 120.7\pm 7.3
\ (r_{\rm d,fid} / r_{\rm d}) \ {\rm km} \ {\rm s}^{-1}{\rm Mpc}^{-1}$ and
$D_M(z=2) = 5325\pm249 \ (r_{\rm d} / r_{\rm d, fid}) \ {\rm Mpc}$, $H(z=2) =
189.9\pm 32.9 \ (r_{\rm d,fid} / r_{\rm d}) \ {\rm km} \ {\rm s}^{-1}{\rm
Mpc}^{-1}$. These measurements are highly correlated. We assess the outlook of
BAO analysis from the final quasar sample by testing the method on a set of
mocks that mimic the noise level in the final sample. We demonstrate on these
mocks that redshift weighting shrinks the measurement error by over 25 per cent
on average. We conclude redshift weighting can bring us closer to the
cosmological goal of the final quasar sample.
