What is the most relevant inflation to monitor?

The question arises as to which definition of inflation is more relevant to monitor, between: Headline inflation; it determines the increase in household purchasing power, but it is biased by the high variability of energy and food prices; Inflation excluding energy and food (excluding energy and unprocessed food in the euro zone), which is not affected by variability in energy and food prices; Inflation excluding energy, food and rents (in the United States, excluding both actual rents and rents imputed to homeowners); the rise in rents is due to the scarcity of rental accommodation; rents imputed to homeowners do not really exist and do not correspond to real consumption; lastly, many European countries control rents, which introduces a bias; The rise in the prices of services excluding rents (actual rents and imputed rents), which is close to wage inflation since it excludes the prices of manufactured goods, which are highly dependent on the prices of energy, industrial metals, maritime transport, etc. When we look empirically at the definition of inflation that has best predicted future total inflation in the medium term, we find that in the United States it is inflation excluding energy, food and rents imputed to homeowners, and in the euro zone it is inflation excluding energy and unprocessed food.