Hodrick-Prescott Filter

The Hodrick-Prescott filter separates a series into a smooth trend and a cyclical component by minimising squared deviations from the trend plus λ times squared second differences of the trend.

Hodrick-Prescott 필터는 추세와의 제곱 편차와 추세 2계 차분의 제곱에 λ를 곱한 값의 합을 최소화해 시계열을 매끄러운 추세와 순환 성분으로 나누는 방법이다.

How can I extract the business-cycle component of quarterly GDP?

분기 GDP에서 경기순환 성분만 뽑아내려면 어떻게 하나요?

The filter chooses the trend that balances closeness to the data against smoothness, with λ controlling the trade-off. Conventional values are 1600 for quarterly, 129600 for monthly and 6.25 for annual data.

When to use Hodrick-Prescott Filter

• You want a smooth trend and a cyclical gap, as in output gap studies.
• The data are macroeconomic series at a standard frequency.
• Comparability with published studies that use HP filtering matters.

When to use something else

• You need real-time estimates at the end of the sample; use a one-sided filter or Hamilton's regression filter.
• The series has strong seasonality; use STL Decomposition first.

Assumptions and requirements

• Trend changes smoothly.
• λ suits the data frequency.
• End-point estimates are less reliable.

What the analysis reports

• Trend and cyclical components
• λ used and inferred frequency
• SD and variance share of the cycle

How to report it

The series was decomposed with a Hodrick-Prescott filter (λ = [value]); the cyclical component had SD = [value].

Related methods

• STL Decomposition
• Kalman Filtering

Run Hodrick-Prescott Filter on Quorant