Using the Arcminute Microkelvin Imager ( AMI ) at 16 GHz and the Very Small Array ( VSA ) at 33 GHz to make follow-up observations of sources in the New Extragalactic WMAP Point Source Catalogue , we have investigated the flux-density variability in a complete sample of 97 sources over timescales of a few months to \approx 1.5 years .

We find that 53 per cent of the 93 sources , for which we have multiple observations , are variable , at the 99 per cent confidence level , above the flux density calibration uncertainties of \approx 4 per cent at 16 GHz ; the fraction of sources having varied by more than 20 per cent is 15 per cent at 16 GHz and 20 per cent at 33GHz .
Not only is this common occurrence of variability at high frequency of interest for source physics , but strategies for coping with source contamination in CMB work must take this variability into account .

There is no strong evidence of a correlation between variability and flux density for the sample as a whole .
For those sources classified as variable , the mean fractional r.m.s .
variation in flux density increases significantly with the length of time separating observation pairs .
Using a maximum-likelihood method , we calculate the correlation in the variability at the two frequencies in a subset of sources classified as variable from both the AMI and VSA data and find the Pearson product-moment correlation coefficient to be very high ( 0.955 \pm 0.034 ) .
We also find the degree of variability at 16 GHz ( 0.202 \pm 0.028 ) to be very similar to that at 33GHz ( 0.224 \pm 0.039 ) .

Finally , we have investigated the relationship between variability and spectral index , \alpha _ { 13.9 } ^ { 33.75 } ( where S \propto \nu ^ { - \alpha } ) , and find a significant difference in the spectral indices of the variable sources ( -0.06 \pm 0.05 ) and non-variable sources ( 0.13 \pm 0.04 ) .