Hide-and-Seek with time-series filters: a model-based Monte Carlo study
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Hide-and-Seek with time-series filters: a model-based Monte Carlo study Vadim Kufenko1 Received: 3 July 2017 / Accepted: 27 May 2019 © Springer-Verlag GmbH Germany, part of Springer Nature 2019
Abstract 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. Keywords Model-based Monte Carlo simulations · Filtering · Spurious inferences · Spurious dynamic relations JEL classification E32 · C18 · C15
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Vadim Kufenko [email protected]
Extended author information available on the last page of the article
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V. Kufenko
1 Introduction Over the last 50 years, time-series filters have become one of the workhorse tools in business cycle research. Detrending has become routine in time-series analysis, one of the many steps for obtaining the cyclical component and performing further inference. However, in the literature one often finds concerns that detrending may yield statistical artifacts and distortions. Although the notion of spuriosity has a wide semantic range, most of these concerns can be traced back to the well-known Gibbs–Wilbraham (Hewitt and Hewitt 1979) and Slutzky–Yule1 effects (Slutzky 1927, 1937; Yule 1927). Another type of distortion addressed by Woitek (1997), Pedersen (2001) and Pollock (2013a, b) is more specific: detrending involving filters
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