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A Steady-State Approach to Trend/Cycle Decomposition of Regime-Switching Processes
We present a new approach to trend/cycle decomposition of time series that follow regime switching processes. The proposed approach, which we label the “regime-dependent steady state” (RDSS) decomposition, is motivated as the appropriate generalization of the Beveridge Nelson (1981) decomposition to the setting where the reduced-form dynamics of a given series can be captured by a regime-switching forecasting model. For processes in which the underlying trend component follows a random walk with possibly regime-switching drift, the RDSS decomposition is optimal in a minimum mean-squared-error sense and is more broadly applicable than directly employing an Unobserved Components model.