This paper examines the implications of detrending macroeconomic time series using the Hodrick-Prescott (HP) filter and evaluates the usefulness of structural time series models in presenting stylized facts. The authors argue that the HP filter, while widely used, can produce spurious cyclical patterns and distort the true cyclical component of a series. Structural time series models, on the other hand, allow for a more accurate decomposition of time series into trend, cycle, and irregular components, and provide a framework for assessing the limitations of other methods such as ARIMA models. The paper presents a structural time series model where the observed series is decomposed into a trend, cycle, and irregular component. The trend is modeled as a local linear trend, while the cycle is modeled as a stationary stochastic process. The model is estimated using maximum likelihood and can be applied to both seasonal and non-seasonal data. The authors show that the HP filter, which is based on a deterministic trend, can lead to misleading conclusions about the cyclical properties of a series, as it imposes a fixed value on the ratio of the variance of the trend and irregular components. The paper also discusses the implications of using the HP filter on various macroeconomic time series, including U.S. real GNP, Austrian real GDP, the U.S. implicit deflator for GNP, and the U.S. monetary base. The authors find that the HP filter can produce detrended series that appear to exhibit cyclical behavior, but this is often spurious and not reflective of the true underlying cycle. They argue that structural time series models provide a more accurate and reliable way of decomposing time series and identifying the true cyclical component. The paper also addresses issues such as seasonality, the limitations of ARIMA models, and the potential for spurious cross-correlations between detrended series. The authors conclude that structural time series models are a more robust and informative approach to analyzing macroeconomic time series, and that the HP filter should be used with caution due to its potential to produce misleading results.This paper examines the implications of detrending macroeconomic time series using the Hodrick-Prescott (HP) filter and evaluates the usefulness of structural time series models in presenting stylized facts. The authors argue that the HP filter, while widely used, can produce spurious cyclical patterns and distort the true cyclical component of a series. Structural time series models, on the other hand, allow for a more accurate decomposition of time series into trend, cycle, and irregular components, and provide a framework for assessing the limitations of other methods such as ARIMA models. The paper presents a structural time series model where the observed series is decomposed into a trend, cycle, and irregular component. The trend is modeled as a local linear trend, while the cycle is modeled as a stationary stochastic process. The model is estimated using maximum likelihood and can be applied to both seasonal and non-seasonal data. The authors show that the HP filter, which is based on a deterministic trend, can lead to misleading conclusions about the cyclical properties of a series, as it imposes a fixed value on the ratio of the variance of the trend and irregular components. The paper also discusses the implications of using the HP filter on various macroeconomic time series, including U.S. real GNP, Austrian real GDP, the U.S. implicit deflator for GNP, and the U.S. monetary base. The authors find that the HP filter can produce detrended series that appear to exhibit cyclical behavior, but this is often spurious and not reflective of the true underlying cycle. They argue that structural time series models provide a more accurate and reliable way of decomposing time series and identifying the true cyclical component. The paper also addresses issues such as seasonality, the limitations of ARIMA models, and the potential for spurious cross-correlations between detrended series. The authors conclude that structural time series models are a more robust and informative approach to analyzing macroeconomic time series, and that the HP filter should be used with caution due to its potential to produce misleading results.