The exact linkage between the Beveridge-Nelson decomposition and other permanent-transitory decompositions

► Analytical relations linking Beveridge-Nelson and unobserved components approaches. ► Exact relation between reduced and structural parameters of trend-cycle models. ► Results are valid regardless of the number of structural/reduced forms parameters. ► Results are provided when using the Hodrick-Prescott filter as detrending method. ► Examples show the use of results for the extraction of the U.S. business cycle.