tokens: over several campaigns (see Raiteri et al. 2013 , and references therein). The data used in this paper come from the WEBT archive. Fig. 2 Nightly averaged -band light curves (Aug. 2008–Jan. 2016) for 0716+714 and MRK 421 from Tuorla Observatory, and for BL Lac obtained combining nightly averaged data from Tuorla (black) and the WEBT observations (violet). The light curves are not host galaxy subtracted. The reported light curves match with the monitoring. Error bars are, in most cases, smaller than symbol size. The relevant nightly averaged light curves matching with the observation span are reported in Fig. 2 . The variability of MRK 421 and BL Lac is up to 5, and for 0716+714 up to a factor 10. The shapes of the light curves are grossly similar to the -ray ones, with fractional variability , 0.30, and 0.43 for 0716+714, MRK 421, and BL Lac, respectively. 3. Search for quasi-periodicities 3.1. Methods Identifying features in periodograms is a delicate task and requires several steps, i.e. a careful modeling of the noise and an analysis of the significance with respect to the noise model. Essentially, we followed the procedure described in Vaughan (2005 , 2010) and Guidorzi et al. (2016) . Power density spectra (PDS) were derived by means of generalized Lomb-Scargle periodograms (e.g. Scargle 1982 ) and, for a cross-check, by means of a completely independent technique ( Huijse et al. 2012 , 2014 ; Protopapas et al. 2015 ) based on a metric that combines the correntropy (generalized correlation) with a periodic kernel to measure similarity among samples separated by a given period. The results obtained with the two techniques are in excellent agreement. We restricted our study to long periods, i.e. in the days interval, where the limits are driven by the length of the considered light-curves, and to avoid the very noisy high-frequency part of the PDS. All the computations are carried out by procedures coded in python 4 (version 3.5.2) language. Statistical tests and functions, as well as optimization tools, are provided by the scipy 5 (V. 0.18.1) library. Lomb-Scargle periodograms are computed by means of the astropy 6 (version 1.2.1) implementation. The so-called correntropy periodograms are computed by the P4J 7 (version 0.13) python library. Leahy normalisation was adopted for the analyses of the PDS ( Leahy et al. 1983 ) while, in the figures, we normalized the resulting PDS to be within the range ( Zechmeister Kürster 2009 ). Fig. 3 From left to right , PDS of 0716+714, MRK 421, and BL Lac from the 100 MeV–300 GeV Fermi light curves, from Aug. 2008 to Jan. 2016. Lomb-Scargle spectrum of the input time-series data is given in blue and the best fit noise spectrum in red. Single frequency 95.0% and 99.7% false alarm levels are reported by purple and yellow lines. Solid and dashed lines refer to PL and AR1 models, respectively. Fig. 4 As above from the -band light curves. The noise was modeled as a simple power law (PL) or as an
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