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A SMOOTHING METHOD THAT LOOKS LIKE THE HODRICK–PRESCOTT FILTER
Econometric Theory ( IF 0.8 ) Pub Date : 2020-03-23 , DOI: 10.1017/s0266466619000379
Hiroshi Yamada

In recent decades, in the research community of macroeconometric time series analysis, we have observed growing interest in the smoothing method known as the Hodrick–Prescott (HP) filter. This article examines the properties of an alternative smoothing method that looks like the HP filter, but is much less well known. We show that this is actually more like the exponential smoothing filter than the HP filter although it is obtainable through a slight modification of the HP filter. In addition, we also show that it is also like the low-frequency projection of Müller and Watson (2018, Econometrica 86, 775–804). We point out that these results derive from the fact that all three similar smoothing methods can be regarded as a type of graph spectral filter whose graph Fourier transform is discrete cosine transform. We then theoretically reveal the relationship between the similar smoothing methods and provide a way of specifying the smoothing parameter that is necessary for its application. An empirical examination illustrates the results.

中文翻译:

一种看起来像 HODRICK-PRSCOTT 过滤器的平滑方法

近几十年来,在宏观计量经济学时间序列分析的研究社区中,我们观察到对称为 Hodrick-Prescott (HP) 滤波器的平滑方法越来越感兴趣。本文研究了另一种平滑方法的属性,该方法看起来像 HP 滤波器,但鲜为人知。我们表明,这实际上更像是指数平滑滤波器而不是 HP 滤波器,尽管它可以通过对 HP 滤波器的轻微修改来获得。此外,我们还展示了它也像 Müller 和 Watson (2018,计量经济学86, 775–804)。我们指出,这些结果源于以下事实:所有三种相似的平滑方法都可以被视为一种图谱滤波器,其图傅里叶变换是离散余弦变换。然后,我们从理论上揭示了类似平滑方法之间的关系,并提供了一种指定其应用所需的平滑参数的方法。实证检验说明了结果。
更新日期:2020-03-23
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