Updating CPI weights through compositional VAR forecasts: an application to the Italian index

Worldwide, monthly CPIs are mostly calculated as weighted averages of price relatives with fixed base weights. The main source of estimation of CPI weights are National Accounts, whose complexity in terms of data collection, estimation of aggregates and validation procedures leads to several months of delay in the release of the figures. This ends up in a non completely consistent Laspeyres formula since the weights do not refer to the same period as the base prices do, being older by one year and then corrected by the elapsed inflation. In this paper we propose to forecast CPI weights via a compositional VAR model, to obtain more updated weights and, consequently, a more updated measure of inflation through CPIs.