Trend–Cycle Decompositions with Correlated Components

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Hysteretic autoregressive time series models (2015, methodology): “Camarero et al. (2006) and Proietti (2006) used nonstationarity to interpret hysteresis in macroeconomic time series, whilst Kannebley (2008) and Perez-Alonso & Sanzo (2011) considered threshold models. c© 2015 Biometrika Trust Biometrika Advance Access published June 9, 2015 at U niversity of H…”
THE TWO INTERPRETATIONS OF THE BEVERIDGE–NELSON DECOMPOSITION (2010, background): “Proietti (2006) and Oh et al. (2008) also consider the observational equivalence between different state-space models related to a reduced-form model ARMA(2,2) for the first differences.”
A Review of Some Modern Approaches to the Problem of Trend Extraction (2012, methodology): “, log-normals), other penalty functions such as Relative MSE may be more appropriate; see Thomson and Ozaki (2002). If we are interested in linear estimators, how do we find the best one? Bell (1984) discusses how these are computed from the autocovariance generating functions of trend and residual,”
The relationship between the Beveridge–Nelson decomposition and other permanent–transitory decompositions that are popular in economics (2008, methodology): “Evaluating ψ(1) and ψ(L) in (8) gives the resulting UC-ARMA(2,1) model parameters in terms of the reduced form ARIMA(2,1,2) model parameters, see Proietti (2006). He shows that ρwv = −1 ifψ(1) > 1 and ρwv = 1 if ψ(1) < 1.”