A state-space approach to calculating the Beveridge-Nelson decomposition

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THE TWO INTERPRETATIONS OF THE BEVERIDGE–NELSON DECOMPOSITION (2010, methodology): “Given the DGPs, this approach is equivalent to solving for the reduced-form forecasting model for each series, casting it into state-space form, and applying the state-space approach to the BN decomposition presented in Morley (2002) to obtain the corresponding BN trend and cycle.”
Why Are the Beveridge-Nelson and Unobserved-Components Decompositions of GDP So Different? (2003, background): “Recent business cycle research suggests that postwar recessions have exhibited important asymmetry; see Neftci (1984), Sichel (1993, 1994), Beaudry and Koop (1993), and Kim and Nelson (1999).”
The Asymmetric Business Cycle (2012, methodology): “Following Kim, Morley, and Piger (2005), we assume m = 6 for the bounceback models, which allows recoveries to persist for up to six quarters following the end of a recession.”
The relationship between the Beveridge–Nelson decomposition and other permanent–transitory decompositions that are popular in economics (2008, methodology): “Therefore, it is possible to test any over-identifying restrictions that are present, although we do not consider that here. extended the method of Morley (2002) for cases in which ∆ 2 y t = z ′ α t , where z is an m × 1 vector with fixed elements and the m × 1 state vector α t follows the…”
Let's take a break: Trends and cycles in US real GDP (2009, unknown): “[30] Morley, J.”