Context. After more than 15 years of quiescence the Be/X-ray binary V0332+53 underwent a giant outburst in December 2004. Aims. We have investigated the timing properties of the source in correlation with its spectral states as defined by different positions in the colour–colour diagram. Methods. We have used RXTE and INTEGRAL light curves to obtain colour–colour diagrams, power spectra and phase-lag spectra. The power spectra were fitted with a multi-Lorentzian function. Results. The source shows two distinct branches in the colour–colour diagram that resemble those of the Z sources. The hard branch (similar to the horizontal branch of Z sources) is characterised by a low-amplitude change of the hard colour compared to the change in the soft colour. In the soft branch (analogue to the normal branch) the amplitude of variability of the hard colour is about three times larger than that of the soft colour. As the count rate decreases the source moves up gradually through the soft to the hard branch. The aperiodic variability (excluding the pulse noise) consists of band-limited noise (represented by three broad Lorentzian components) and two QPOs at 0.05 Hz and 0.22 Hz. The strength of the lower frequency QPO increases as the source approaches the hard branch (similar to HBOs in Z sources). The higher frequency QPO reaches maximum significance when the source is in the middle of the branch (like NBOs).We have performed the first measurements of phase lags in the band limited noise below 8 Hz in an accreting X-ray pulsar and found that soft lags dominate at high frequencies. Above the pulse frequency (0.23 Hz), the amplitude of the lag increases as the X-ray flux increases. Conclusions. The Z topology appears to be a signature of the neutron star binaries as it is present in all types of neutron-star binaries (Z, atoll and, as we show here, in accreting pulsars as well). However, the motion along this track, the time scales through the different branches of the diagram and the aperiodic variability associated with portions of the Z track differ for each subclass of neutron-star binary.