The more massive counterparts of T Tauri stars, Herbig Ae/Be stars, are known to vary in a complex way with no variability mechanism clearly identified. We attempt to characterize the optical variability of HD~37806 (MWC 120) on time scales ranging between minutes and several years. A continuous, one-minute resolution, 21 day-long sequence of MOST (Microvariability & Oscillations of STars) satellite observations has been analyzed using wavelet, scalegram and dispersion analysis tools. The MOST data have been augmented by sparse observations over 9 seasons from ASAS (All Sky Automated Survey), by previously non-analyzed ESO (European Southern Observatory) data partly covering 3 seasons and by archival measurements dating back half a century ago. Mutually superimposed flares or accretion instabilities grow in size from about 0.0003 of the mean flux on a time scale of minutes to a peak-to-peak range of <~0.05 on a time scale of a few years. The resulting variability has properties of stochastic red noise, whose self-similar characteristics are very similar to those observed in cataclysmic binary stars, but with much longer characteristic time scales of hours to days (rather than minutes) and with amplitudes which appear to cease growing in size on time scales of tens of years. In addition to chaotic brightness variations combined with stochastic noise, the MOST data show a weakly defined cyclic signal with a period of about 1.5 days, which may correspond to the rotation of the star.
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