Hide-and-Seek with time-series filters: a model-based Monte Carlo study

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.