In an attempt to constrain and understand the emission mechanism of γ rays, we perform a cross-correlation analysis of 15 blazars using light curves in millimetre, optical and γ rays. We use discrete correlation function and consider only correlations significant at 99 per cent level. A strong correlation was found between 37 and 95 GHz with a near-zero time delay in most of the sources, and ∼1 month or longer in the rest. A similar result was obtained between the optical and γ-ray bands. Of the 15 sources, less than 50 per cent showed a strong correlation between the millimetre and γ-ray or millimetre and optical bands. The primary reason for the lack of statistically significant correlation is the absence of a major outburst in the millimetre bands of most of the sources during the 2.5 yr time period investigated in our study. This may indicate that only the long-term variations or large flares are correlated between these bands. The variability of the sources at every waveband was also inspected using fractional rms variability (Fvar ). The Fvar displays an increase with frequency reaching its maximum in the γ rays.