SNIP

I also noticed that at least with the basement faucet I was testing,
there is a delay of 3 - 4 seconds before the thumping starts after the
faucet is shut. I had time to walk across the basement to the incoming
meter after shutting the faucet before the thumps started. It is
during this time that I can still hear the water flowing in the pipes
even after the faucet is closed.

SNIP

If you can hear water flowing after you shut the faucet off, then to me,
that is a strong indication of air in the system. Perhaps the combination
of air and a malfunctioning pressure reducing valve is why there are
multiple thumps.
MLD