The Use of Butterworth Filters for Trend and Cycle Estimation in Economic Time Series
The Use of Butterworth Filters for Trend and Cycle Estimation in Economic Time Series
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使用巴特沃斯滤波器进行经济时间序列的趋势和周期估计
DOI：
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发表时间：
2001
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通讯作者：
Víctor Gómez
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文献类型：
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作者：
Víctor Gómez
长期趋势和商业周期通常通过对X-11季节调整数据应用Hodrick和Prescott （HP）过滤器来估计。本文提出了一个两阶段的程序来改进这一方法。改进是基于(a)使用Butterworth滤波器或专门为当前问题设计的带通滤波器作为HP滤波器的替代方案，(b)将选定的滤波器应用于估计的趋势周期，而不是季节性调整的序列，以及(c)使用自回归集成移动平均模型通过预测和反推算来扩展输入序列。文中显示，HP过滤器是Butterworth过滤器，如果使用基于模型的方法进行季节调整，则可以对所建议的程序给出完全基于模型的解释。在这种情况下，可以计算预测和估计趋势和周期的均方误差。用几个例子说明了这个过程。
Long-term trends and business cycles are usually estimated by applying the Hodrick and Prescott (HP) filter to X-11 seasonally adjusted data. A two-stage procedure is proposed in this article to improve this methodology. The improvement is based on (a) using Butterworth or band-pass filters specifically designed for the problem at hand as an alternative to the HP filter, (b) applying the selected filter to estimated trend cycles instead of to seasonally adjusted series, and (c) using autoregressive integrated moving average models to extend the input series with forecasts and backcasts. It is shown in the article that the HP filter is a Butterworth filter and that, if a model-based method is used for seasonal adjustment, it is possible to give a fully model-based interpretation of the proposed procedure. In this case, one can compute forecasts and mean squared errors of the estimated trends and cycles. The procedure is illustrated with several examples.