In his article, Hamilton (2017) conveyed a critique of the Hodrick-Prescott (HP) filter, arguing against its utilization due to several inherent issues. He emphasizes that the filter’s sensitivity to the smoothing parameter selection, its tendency to generate misleading cycles, and its failure to accurately represent the actual underlying trend are significant drawbacks. While I partially concur with Hamilton’s viewpoint, it is essential to note that both filters offer distinct perspectives on the cyclical characteristics of the data, and it might be interesting to rethink certain aspects of Hamilton’s arguments.
Firstly, it is argued that the HP filter leads to a series of misleading dynamic associations, which lack a foundation in the underlying data-generating process. The underlying critique of the HP filter revolves around its tendency to impose dynamic patterns that are not connected to how the data is generated. While one might accept the notion of a random walk on a trend, relying solely on asymptotic statistics may not always yield definitive results. Nonetheless, it is worth noting that such series rarely emerge, allowing the HP-detrended series to demonstrate reliable forecasting capabilities (Dritsaki & Dritsaki, 2022).
Secondly, the critique argues that the HP filter yields significantly different filtered values at the end of the sample compared to the middle, leading to spurious dynamics. However, this bias may not be a concern when detrending targets specific business cycle events and is not used for real-time analysis or macroeconomic forecasts (Dritsaki & Dritsaki, 2022). Despite these shortcomings, the HP filter can still be useful with two adjustments, a lower smoothing parameter and rescaling of the extracted cyclical component (Wolf et al., 2020). However, this point of critique is relevant to the filter’s capability to create cycles where they do not exist. Previous studies (Nelson & Kang, 1981; Cogley & Nason, 1995) have shown that linear detrending of a random walk time series can induce spurious periodicity and complex dynamic properties in cyclical components that seemingly do not exist.
Thirdly, it is argued that when statistically formalizing the problem, the smoothing parameter (𝜆) values vastly differ from common practice. Hamilton contends that for quarterly data, a 𝜆 value below 1600 results in the last component of the trend-cycle decomposition being considered white noise. He proposes estimating 𝜆 using the maximum likelihood method and advocates setting the highest value for the 𝜆 coefficient to address excessive flexibility in the trend line. Nonetheless, Schuler (2018) demonstrates that the Hamilton regression filter possesses some drawbacks in common with the Hodrick-Prescott filter, such as the cancellation of two-year cycles and the amplification of longer cycles than typical business cycles, leading to inconsistencies with typical business cycle facts recognized by the National Bureau of Economic Research Studies (NBER) Business Cycle Dating Committee.
As an alternative to the Hodrick-Prescott (HP) filter, Hamilton proposes a robust detrending approach by regressing the variable at date t+h on the four most recent values as of date t. This approach is deemed superior to the HP filter as it avoids spurious dynamic relations and dynamics, providing more stable estimates of the underlying trend. Business cycle information could be extracted directly from time series using suitably selected forecasting OLS error from an autoregression model. Moreover, the approach offers greater flexibility by involving additional variables in the regression as necessary (Dritsaki & Dritsaki, 2022).
Nevertheless, the proposed alternative filter by Hamilton faces similar criticisms as the HP filter, including the presence of filter-induced dynamics in estimated cycles and the arbitrary nature of a key parameter choice (Moura, 2022). Moreover, the Hamilton approach’s estimated trends inherently lag the data, raising doubts about its claimed superiority over the HP filter in practice. Recent empirical research also shows that the HP filter outperforms Hamilton’s filter in dynamic forecasting, with significantly smaller cycle volatilities (Dritsaki and Dritsaki, 2022). The HP or Hamilton filter would inherently produce distinct estimates of the cyclical component. However, this issue becomes less significant when relating stationary economic models to non-stationary data, as comparisons between filtered real-world data and model-filtered series are feasible (Burnside, 1998).
In conclusion, both filters offer distinct perspectives on the cyclical properties of the data, with no clear superiority. As Hodrick (2020) proposes, future research could focus on developing simultaneous multivariate econometric models that apply filters for decomposing trends and cyclical components present in economic data, influencing the development of business cycles.
References
Burnside, C. (1998). Detrending and business cycle facts: A comment. Journal of Monetary Economics, 41(3), 513-532.
Cogley, T., & Nason, J. M. (1995). Effects of the Hodrick-Prescott filter on trend and difference stationary time series: Implications for business cycle research. Journal of Economic Dynamics and Control, 19(1-2): 253-278.
Dritsaki, M., & Dritsaki, C. (2022). Comparison of HP Filter and the Hamilton’s Regression. Mathematics, 10(8):1237.
Hamilton, J. (2017, June 22). Why you should never use the Hodrick-Prescott filter. Centre for Economic Policy Research. https://cepr.org/voxeu/columns/why-you-should-never-use-hodrick-prescott-filter.
Hamilton, J. (2018). Why you should never use the Hodrick-Prescott filter. Review of Economics and Statistics, 100(5), 831-843.
Hodrick, R. J. (2020). An Exploration of Trend-Cycle Decomposition Methodologies in Simulated Data. National Bureau of Economic Research, Working Paper No. 26750.
Moura, A. (2022). Why you should never use the Hodrick-Prescott filter: Comment. MPRA Paper, No.114922
Nelson, C., & Kang, H. (1981). Spurious Periodicity in Inappropriately Detrended Time Series. Econometrica, 49, 741–751.
Schuler, Y. S. (2018). On the Cyclical Properties of Hamilton’s Regression Filter. Deutsche Bundesbank Discussion Paper 03/2018.
Wolf, E., Mokinski, F., & Schüler, Y. (2020). On Adjusting the One-Sided Hodrick–Prescott Filter. Deutsche Bundesbank Discussion Paper No. 11/2020.
hope. 