The BL Lacertae object AO 0235+16 is well known for its extreme optical and radio variability. New optical and radio data have been collected in the last four years by a wide international collaboration, which confirm the intense activity of this source: on the long term, overall variations of 5mag in the R band and up to a factor 18 in the radio fluxes were detected, while short-term variability up to 0.5mag in a few hours and 1.3mag in one day was observed in the optical band. The optical data also include the results of the Whole Earth Blazar Telescope (WEBT) first-light campaign organized in November 1997, involving a dozen optical observatories. The optical spectrum is observed to basically steepen when the source gets fainter. We have investigated the existence of typical variability time scales and of possible correlations between the optical and radio emissions by means of visual inspection and Discrete Correlation Function (DCF) analysis. On the long term, the autocorrelation function of the optical data shows a double-peaked maximum at 4100-4200 days (11.2-11.5 years), while a double-peaked maximum at 3900-4200 days (10.7-11.5 years) is visible in the radio autocorrelation functions. The existence of this similar characteristic time scale of variability in the two bands is by itself an indication of optical-radio correlation. A further analysis by means of Discrete Fourier Transform (DFT) technique and folded light curves reveals that the major radio outbursts repeat quasi-regularly with a periodicity of ~ 5.7 years, i.e. half the above time scale. This period is also in agreement with the occurrence of some of the major optical outbursts, but not all of them. Visual inspection and DCF analysis of the optical and radio light curves then reveal that in some cases optical outbursts seem to be simultaneous with radio ones, but in other cases they lead the radio events. Moreover, a deep inspection of the radio light curves suggests that in at least two occasions (the 1992-1993 and 1998 outbursts) flux variations at the higher frequencies may have led those at the lower ones.