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Fully Modified HP Filter


  • Muhammad Nadim Hanif

    () (State Bank of Pakistan)

  • Javed Iqbal

    () (State Bank of Pakistan)

  • M. Ali Choudhary

    () (State Bank of Pakistan)


Business cycle estimation is core of macroeconomics research. Hodrick-Prescott (1997) filter, (or HP filter), is the most popular tool to extract cycle from a macroeconomic time series. There are certain issues with HP filter including fixed value of ? across the series/countries and end points bias (EPB). Modified HP filter (MHP) of McDermott (1997) attempted to address the first issue. Bloechl (2014) introduced a loss function minimization approach to address the EPB issue but keeping lambda fixed (as in HP filter). In this study we marry the endogenous lambda approach of McDermott (1997) with loss function minimization approach of Bloechl (2014) to analyze EPB in HP filter, while intuitively changing the weighting scheme used in the latter. We contribute by suggesting an endogenous weighting scheme along with endogenous smoothing parameter to resolve EPB issue of HP filter. We call this fully modified HP (FMHP) filter. Our FMHP filter outperforms a variety of conventional filters in a power comparison (simulation) study as well as in observed real data (univariate and multivariate) analytics for a large set of countries.

Suggested Citation

  • Muhammad Nadim Hanif & Javed Iqbal & M. Ali Choudhary, 2017. "Fully Modified HP Filter," SBP Working Paper Series 88, State Bank of Pakistan, Research Department.
  • Handle: RePEc:sbp:wpaper:88

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    More about this item


    Business Cycle; Time Series; Fully Modified HP Filter; End Point Bias in HP Filter; Simulation; Cross Country Study.;

    JEL classification:

    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General

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