Within the MOJAVE VLBA programme (Monitoring of Jets in AGN with VLBA Experiments), we have accumulated observational data at 15 GHz for hundreds of jets in gamma-ray bright active galactic nuclei since the beginning of the Fermi scientific observations in 2008 August. We investigated a time delay between the flux density of AGN parsec-scale radio emission at 15 GHz and 0.1-300 GeV Fermi LAT photon flux, taken from constructed light curves using weekly and adaptive binning. The correlation analysis shows that radio is lagging gamma-ray radiation by up to 8 months in the observer's frame, while in the source frame, the typical delay is about 2-3 months. If the jet radio emission, excluding the opaque core, is considered, significant correlation is found at greater time lags. We supplement these results with VLBI kinematics and core shift data to conclude that the dominant high-energy production zone is typically located at a distance of several parsecs from the central nucleus. We also found that quasars have on average more significant correlation peak, more distant gamma-ray emission region from the central engine and shorter variability time-scale compared to those of BL Lacertae objects.