Comparison of HP Filter and the Hamilton’s Regression

Abstract

In this paper we examine if the use of Hamilton’s regression filter significantly modifies the cyclical components concerning unemployment in Greece compared with those using the Hodrick–Prescott double filter (HP). Hamilton suggested the use of a regression filter in order to overcome some of the drawbacks of the HP filter, which contains the presence of false cycles, the bias in the end of the sample, and the ad-hoc assumptions for the parameters’ smoothing. Thus, our paper examines two widely used detrending methods for the extraction of cyclical components, including techniques of deterministic detrending as well as stochastic detrending. Using quarterly data for the unemployment of Greece in a macroeconomic model decomposition, we indicate that trend components and cycle components of Hamilton’s filter regression led to significantly larger cycle volatilities than those from the HP filter. The dynamic forecasting in the sample, occurred both with autoregressive forecasting, that yields steady forecasts for a wide variety of non-stationary procedures, and with the HP filter, along with its constraints at the end of the time series. The results of the paper showed that the dynamic forecasting of the HP filter is better than that of Hamilton’s in all assessment measures.

A hybrid forecasting technique for infection and death from the mpox virus

“…In the recent case, the study variable C t is explained by the previous n terms, the lagged values of residuals as well. 42 Mathematically, represents the average value of the model; and denote the parameters of the ARMA processes, respectively; and is normally distributed with white noise with constant mean and variance. Model selection of ARMA is guessed by inspecting the correlograms.…”

“…They concluded that by using the appropriate methods that are suitable to the data, one can achieve consistent results in modelling and predicting any series of an epidemic. For more epidemic hybrid time series forecasting, see, for example, 34 – 42 .…”

Smooth Forecast Reconciliation

“…For example, Hamilton (2018) proposes Maximum Likelihood estimates and points out drawbacks of the HP filter, including the endpoint problem. Hodrick (2020) and Dritsaki and Dritsaki (2022) offer counterarguments. Instead of assuming a data-generating process and discussing whether the HP filter estimates the trend accurately, this paper interprets the HP filter as a smoothing device and uses actual data to check the forecast performance.…”

Cyclical Consumption, Real Interest Rate Deviations and Output Gaps in a Large Emerging Economy: Expected and Unexpected Responses under Different Regimes

“…There could be biases in the estimation of cycles, especially at the end of the sample, as well as the alleged issue of ad hoc choice for the smoothing parameter. Despite subsequent works (Jonsson, 2020;Phillips & Shi, 2021, among others) criticizing Hamilton's (2018) arguments and even yielding results in favor of using the HP filter (such as in Dritsaki & Dritsaki, 2022), this study preferred to perform a robustness test based on the estimation of cyclical components using the method proposed in Hamilton (2018). Essentially, Hamilton (2018) proposed a method for extracting the cyclical component of a variable Z based on its forecast over t h + periods ahead, using the four most recent values of the own time series Z.…”