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Among active galactic nuclei, blazars show extreme variability properties. Wehere investigate the case of the BL Lac object S4 0954+65 with data acquired in2019-2020 by the Transiting Exoplanet Survey Satellite (TESS) and by the WholeEarth Blazar Telescope (WEBT) Collaboration. The 2-min cadence optical lightcurves provided by TESS during three observing sectors of nearly one montheach, allow us to study the fast variability in great detail. We identifyseveral characteristic short-term time-scales, ranging from a few hours to afew days. However, these are not persistent, as they differ in the various TESSsectors. The long-term photometric and polarimetric optical and radiomonitoring undertaken by the WEBT brings significant additional information,revealing that i) in the optical, long-term flux changes are almost achromatic,while the short-term ones are strongly chromatic; ii) the radio flux variationsat 37 GHz follow those in the optical with a delay of about three weeks; iii)the range of variation of the polarization degree and angle is much larger inthe optical than in the radio band, but the mean polarization angles aresimilar; iv) the optical long-term variability is characterized by aquasi-periodicity of about one month. We explain the source behaviour in termsof a rotating inhomogeneous helical jet, whose pitch angle can change in time.

The complex variability of blazars: Time-scales and periodicity analysis in S4 0954+65