for the current state regardless of the size of used. The standard two-sided Hodrick–Prescott filter is non-causal as it is not purely backward looking. Hence, it should not be used when estimating DSGE models based on recursive state-space representations (e.g., likelihood-based methods that make use of the Kalman filter). The reason is that the Hodrick–Prescott filter uses observations at to construct the current time point , while the recursive setting assumes that only current and past states influence the current observation. One way around this is to use the one-sided Hodrick–Prescott filter. Exact algebraic formulas are available for the two-sided Hodrick–Prescott filter in terms of its signal-to-noise ratio . A working paper by James D. Hamilton at UC San Diego titled "Why You Should Never Use the Hodrick-Prescott Filter" presents evidence against using the HP filter. Hamilton writes that: The HP filter produces series with spurious dynamic relations that have no basis in the underlying data-generating process. A one-sided version of the filter reduces but does not eliminate spurious predictability and moreover produces series that do not have the properties sought by most potential users of the HP filter. A statistical formalization of the problem typically produces values for the smoothing parameter vastly at odds with common practice, e.g., a value for λ far below 1600 for quarterly data. There’s a better alternative. A regression of the variable at date t+h on the four most recent values as of date t offers a robust approach to detrending that achieves all the objectives sought by users of the HP filter with none of its drawbacks." A working paper by Robert J. Hodrick titled "An Exploration of Trend-Cycle Decomposition Methodologies in Simulated Data" examines whether the proposed alternative approach of James D. Hamilton is actually better than the HP filter at extracting the cyclical component of several simulated time series calibrated to approximate U.S. real GDP. Hodrick finds that for time series in which there are distinct growth and cyclical components, the HP filter comes closer to isolating the cyclical component than the Hamilton alternative. See also Band-pass filter Kalman filter References Further reading External links a freeware Hodrick Prescott Excel Add-In Prescott's Fortran code Hodrick–Prescott filter in matlab One-sided Hodrick–Prescott filters in matlab HP filter in R with package 'mFilter' HP filter online app One-sided Hodrick-Prescott filter in Excel Time series