The Multistep Beveridge-Nelson decomposition

The Beveridge–Nelson decomposition defines the trend component in terms of the eventual forecast function, as the value the series would take if it were on its long-run path. The article introduces the multistep Beveridge–Nelson decomposition, which arises when the forecast function is obtained by the direct autoregressive approach, which optimizes the predictive ability of the AR model at forecast horizons greater than one. We compare our proposal with the standard Beveridge–Nelson decomposition, for which the forecast function is obtained by iterating the one-step-ahead predictions via the chain rule. We illustrate that the multistep Beveridge–Nelson trend is more efficient than the standard one in the presence of model misspecification, and we subsequently assess the predictive validity of the extracted transitory component with respect to future growth.