This paper uses simulations to explore the properties of the HP filter of Hodrick and Prescott (1997), the BK filter of Baxter and King (1999), and the H filter of Hamilton (2018) that are designed to decompose a univariate time series into trend and cyclical components. Each simulated time series approximates the natural logarithms of U.S. Real GDP, and they are a random walk, an ARIMA model, two unobserved components models, and models with slowly changing nonstationary stochastic trends and definitive cyclical components. In basic time series, the H filter dominates the HP and BK filters in more closely characterizing the underlying framework, but in more complex models, the reverse is true.
Hodrick, Robert. "An Exploration of Trend-Cycle Decomposition Methodologies in Simulated Data." Columbia Business School and NBER, February 2020.
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