A simple estimate of the photometric redshift would prove invaluable to forthcoming continuum surveys on the next generation of large radio telescopes, as well as mitigating the existing bias towards the most optically bright sources. While there is a well known correlation between the near-infrared K-band magnitude and redshift for galaxies, we find the K-z relation to break down for samples dominated by quasi-stellar objects (QSOs). We hypothesise that this is due to the additional contribution to the near-infrared flux by the active galactic nucleus (AGN), and, as such, the K-band magnitude can only provide a lower limit to the redshift in the case of active galactic nuclei, which will dominate the radio surveys. From a large optical dataset, we find a tight relationship between the rest-frame (U-K)/(W2-FUV) colour ratio and spectroscopic redshift over a sample of 17,000 sources, spanning z ~ 0.1 - 5. Using the observed-frame ratios of (U K)/(W2-FUV) for redshifts of z > 1, (I-W2)/(W3-U) for 1 < z < 3 and (I-W2.5)/(W4-R) for z > 3, where W2.5 is the 8.0 micron magnitude and the appropriate redshift ranges are estimated from the W2 (4.5 micron) magnitude, we find this to be a robust photometric redshift estimator for quasars. We suggest that the rest-frame U-K colour traces the excess flux from the AGN over this wide range of redshifts, although the W2-FUV colour is required to break the degeneracy.
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