Time-series filters have become a major tool for univariate and multivariate analysis of business cycles. Yet, the caveats of filtering, such as distortions in spectral density often mentioned in the literature, may have substantial implications for empirical analysis. This paper focuses on two main problems: univariate and multivariate spurious inferences. While detrending the real world data, the true cyclical component is unknown, which makes it problematic to assess the efficiency of time-series filters. Using model-based Monte Carlo simulations solves this issue by introducing four different scenarios with a known trend, cyclical components and shocks. The goal of this exercise is to create realistic long-run macroeconomic time-series. To assess the performance of the five well-established time-series filters, spectral densities of the detrended fluctuations are analyzed and changes in the cross-correlation structure and deviations from the original implied fluctuations are examined. Analysis confirms and complements findings from the existing literature and provides some new insights: (i) presence of the Gibbs–Wilbraham phenomenon (for the Christiano–Fitzgerald and Baxter–King filters), yet no obvious evidence of the Slutzky–Yule phenomenon; (ii) the erroneous choice of filtering bands may lead to spurious inferences about the spectral density peaks of the detrended fluctuations; (iii) preservation of the spectral pattern of the original regular and irregular components after detrending with minor changes in the magnitude of the spectral density peaks; (iv) substantial outlier changes in the cross-correlation structure. The latter distortion may have far-reaching implications for further time-series analysis and may lead to spurious inferences about the interaction between the detrended series.

中文翻译：

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具有时间序列过滤器的“ 捉迷藏” ：基于模型的蒙特卡洛研究

时间序列过滤器已成为对业务周期进行单变量和多变量分析的主要工具。然而，滤波的注意事项，如文献中经常提到的频谱密度失真，可能对经验分析有重大影响。本文着重于两个主要问题：单变量和多变量虚假推断。在消除现实世界数据趋势时，真正的周期性成分是未知的，这使得评估时序滤波器的效率成为问题。使用基于模型的蒙特卡洛模拟通过引入四种具有已知趋势，周期性分量和冲击的不同情况来解决此问题。此练习的目的是创建现实的长期宏观经济时间序列。要评估五个公认的时间序列过滤器的性能，分析了去趋势波动的频谱密度，并检查了互相关结构的变化以及与原始隐含波动的偏差。分析证实并补充了现有文献的发现，并提供了一些新的见解：（i）存在吉布斯-威尔布拉汉现象（对于克里斯蒂安诺-菲茨杰拉德和巴克斯特-金过滤器），但尚无明显的鲁兹基-尤尔现象证据；（ii）错误选择滤波频带可能导致关于去趋势波动的频谱密度峰值的虚假推论；（iii）在去趋势化后保留原始规则和不规则成分的光谱图样，并且光谱密度峰值的幅度发生微小变化；（iv）互相关结构发生明显的离群值变化。