Comparative analysis of the cyclical components of Russia’s GDP using the Hodrick-Prescott, Baxter-King, and Christiano-Fitzgerald Methods

Background. Fluctuations in economic activity remain a key focus of macroeconomic analysis, as the phases of the business cycle reflect the economy’s response to external and internal shocks. For Russia, this topic is particularly relevant due to repeated crisis episodes over the past two decades and the need for reliable tools to diagnose phases of growth and recession. A comparison of time-series filtering methods makes it possible to identify which of them provide the most accurate assessment of cyclical fluctuations in GDP.

Purpose – is to conduct a comparative analysis of the cyclical components of Russia’s real GDP extracted using the Hodrick-Prescott (HP), Baxter-King (BK), and Christiano-Fitzgerald (CF) filters.

Materials and methods. Quarterly Russian GDP data for 2003 - 3rd quarter 2025 (at 2021 prices, seasonally adjusted) were obtained from Rosstat. The study employed econometric and statistical methods of time-series analysis: the HP, BK, and CF filters implemented in the Statsmodels package (Python).

Results. The analysis showed that all three methods consistently capture the main recessions in the modern Russian economy – 2009, 2015-2016, and 2020. The BK and CF filters produce nearly identical cyclical trajectories, with a correlation coefficient of about 0.97, indicating their statistical equivalence in business-cycle estimation.

The HP filter generates a higher-frequency, noisier component and smooths the negative phases at the series ends due to the endpoint problem. This results in lower accuracy when identifying short-term downturns (about 75% of crisis quarters compared to 100% for BK and CF).

The extracted cycles reproduce the well-known recessionary periods: the sharp GDP decline in 2009, the contraction in 2015–2016, and the 2020 downturn are captured by all three methods. Band-pass filters (BK and CF) provide a more realistic dynamic that reflects the duration and depth of crisis phases, while HP smooths amplitudes and accelerates the transition to recovery. The novelty of the study lies in the comparative evaluation of three classical filters using a modern Russian dataset, including the most recent observations, and in the quantitative assessment of their ability to accurately detect crisis episodes.

Practical implications. The results can be used for business cycle analysis, assessment of deviations of actual GDP from potential levels, macroeconomic forecasting, and the development of anti-crisis economic policy measures.