Hodrick-Prescott Filter: Trend-Cycle Decomposition for Macroeconomic Time Series
Hodrick-Prescott Filter · Also known as: Hodrick-Prescott Filter, HP Decomposition, Trend-Cycle Filter, HP Filtresi
The Hodrick-Prescott (HP) filter is a penalized least-squares technique used in macroeconomics and empirical finance to decompose a time series into a smooth long-run trend component and a short-run cyclical component. Introduced by Hodrick and Prescott (1997) using postwar U.S. business cycle data, it has become one of the most widely applied filters in business cycle analysis, monetary policy research, and applied econometrics.
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When to use it
The HP filter is appropriate when the research objective is to decompose a macroeconomic or financial time series into trend and cycle, particularly for business cycle analysis, output gap measurement, or potential output estimation. It assumes the series is non-stationary with a slowly evolving trend and short-run cyclical deviations. Key assumptions are additivity of trend and cycle and a user-specified lambda consistent with the data frequency. It is less suitable for series with structural breaks, near-unit-root behavior, or end-point sensitivity concerns. Alternatives include the Baxter-King filter, STL decomposition, and Kalman-filter-based state-space models.
Strengths & limitations
- Simple closed-form computation requiring no iterative estimation; computationally fast even for long series.
- Flexible across data frequencies through the lambda parameter (100/1600/14400 for annual/quarterly/monthly).
- Produces interpretable, smooth trend series widely understood by policymakers and central bank economists.
- Easily replicated and comparable across studies, facilitating cross-country and cross-period business cycle research.
- The choice of lambda is arbitrary and mechanical; results can vary substantially with different lambda values.
- End-point problem: trend estimates near the beginning and end of the sample are unreliable due to asymmetric data availability.
- Hamilton (2018) shows the HP filter can introduce spurious cycles into white-noise series, questioning its statistical validity.
- Sensitive to unit roots and structural breaks; may produce misleading cycles when underlying data-generating process is misspecified.
Frequently asked
How do I choose the lambda parameter?
The conventional values recommended by Hodrick and Prescott are 100 for annual data, 1600 for quarterly data, and 14400 for monthly data. These were calibrated so that the ratio of business-cycle variance to trend variance matches empirical priors. For non-standard frequencies or specific research questions, some authors derive lambda via the formula lambda = 6.25 * (frequency ratio)^4, following Ravn and Uhlig (2002).
What is the end-point problem and how can I address it?
Because the HP filter is a two-sided filter, the trend estimates at the start and end of the sample depend on data that do not yet exist. This creates substantial revisions as new observations arrive. Common remedies include extending the sample with forecasted values before filtering, using one-sided variants of the filter for real-time applications, or switching to alternative filters such as the Hamilton (2018) regression-based approach that avoids the end-point issue.
Is the HP filter still acceptable given Hamilton's (2018) critique?
Hamilton (2018) demonstrated that the HP filter applied to unit-root processes induces spurious cycles even in white noise, and proposed a simple OLS regression alternative. Despite this critique, the HP filter remains widely used in policy institutions and comparative studies due to its computational simplicity and legacy. Researchers should acknowledge its limitations, complement results with alternative methods, and avoid strong structural interpretations of the extracted cycle component.
Sources
- Hodrick, R. J., & Prescott, E. C. (1997). Postwar U.S. business cycles: An empirical investigation. Journal of Money, Credit and Banking, 29(1), 1–16. DOI: 10.2307/2953682 ↗
How to cite this page
ScholarGate. (2026, June 2). Hodrick-Prescott Filter. ScholarGate. https://scholargate.app/en/econometrics/hp-filter
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
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