This research memorandum, authored by Andrew C. Harvey and Albert Jaeger, explores the implications of detrending techniques, particularly the Hodrick-Prescott (HP) filter, on macroeconomic time series data. The authors argue that structural time series models provide a more reliable framework for presenting stylized facts about economic data compared to methods like ARIMA models and mechanical detrending techniques. They demonstrate that the HP filter can lead to spurious cyclical behavior and distorted estimates of the cyclical component, especially when applied to series with non-stationary components. The study also examines the limitations of ARIMA methodology and models based on deterministic trends with single breaks. Through empirical examples using U.S. and Austrian GDP, deflators, and monetary base data, the authors illustrate how the HP filter can misrepresent the underlying economic dynamics. The memorandum concludes by emphasizing the importance of simultaneous estimation of trends and cycles within structural models to avoid such pitfalls and to provide a more accurate representation of the stylized facts in macroeconomic time series.This research memorandum, authored by Andrew C. Harvey and Albert Jaeger, explores the implications of detrending techniques, particularly the Hodrick-Prescott (HP) filter, on macroeconomic time series data. The authors argue that structural time series models provide a more reliable framework for presenting stylized facts about economic data compared to methods like ARIMA models and mechanical detrending techniques. They demonstrate that the HP filter can lead to spurious cyclical behavior and distorted estimates of the cyclical component, especially when applied to series with non-stationary components. The study also examines the limitations of ARIMA methodology and models based on deterministic trends with single breaks. Through empirical examples using U.S. and Austrian GDP, deflators, and monetary base data, the authors illustrate how the HP filter can misrepresent the underlying economic dynamics. The memorandum concludes by emphasizing the importance of simultaneous estimation of trends and cycles within structural models to avoid such pitfalls and to provide a more accurate representation of the stylized facts in macroeconomic time series.