Variability of a galaxys core radio source can be a significant consequence of AGN accretion. However, this variability has not been well studied, particularly at high radio frequencies. As such, we report on a campaign monitoring the high radio frequency variability of 20 nearby, cool-core brightest cluster galaxies. Our highest cadence observations are at 15 GHz and are from the Owens Valley Radio Observatory (OVRO). They have a median time interval of 7 days and mostly span between 8 and 13 years. We apply a range of variability detection techniques to the lightcurves of the sources to analyse changes in their flux density on week to decade long timescales. Over the full period in which each source was observed, $chi^{2}$ tests suggest that 13/20 are inconsistent with the flat lightcurve of a non-varying source. Variability amplitude tests suggest that 12/20 sources are variable on 300 day timescales, while 19/20 are variable on 3000 day timescales. At least half of the sources also show 20 per cent peak to trough variability on 3~year timescales, while at least a third vary by 60 per cent on 6~year timescales. Significant variability is therefore a common feature of these sources. We also show how the variability relates to spectral properties at frequencies of up to 353 GHz using data from the Korean VLBI network (KVN), the NIKA2 instrument of the IRAM 30m telescope, and the SCUBA-2 instrument of the James Clerk Maxwell Telescope.
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