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Radio and $γ$-ray activity in the jet of the blazar S5 0716$+$714

We explore the connection between the $γ$-ray and radio emission in the jet of the blazar 0716$+$714 by using 15, 37, and 230 GHz radio and 0.1$-$200 GeV $γ$-ray light curves spanning 10.5 years (2008$-$2019). We find significant positive and negative correlations between radio and $γ$-ray fluxes in different time ranges. The time delays between radio and $γ$-ray emission suggest that the observed $γ$-ray flares originated from multiple regions upstream of the radio core, within a few parsecs from the central engine. Using time-resolved 43 GHz VLBA maps we identified 14 jet components moving downstream along the jet. Their apparent speeds range from 6 to 26 $c$, showing notable variations in their position angles upstream the stationary component ($\sim$0.53 mas from the core). The brightness temperature declines as function of distance from the core according to a power-law which becomes shallower at the location of the stationary component. We also find that the periods at which significant correlations between radio and $γ$-ray emission occur overlap with the times when the jet was oriented to the north. Our results indicate that the passage of a propagating disturbance (or shock) through the radio core and the orientation of the jet might be responsible for the observed correlation between the radio and $γ$-ray variability. We present a scenario that connects the positive correlation and the unusual anti-correlation by combining the production of a flare and a dip at $γ$-rays by a strong moving shock at different distances from the jet apex.