The Hodrick–Prescott (HP) filter has been a popular method of trend extraction from economic time series. However, it is impractical without modification if some observations are not available. This paper improves the HP filter so that it can be applied in such situations. More precisely, this paper introduces two alternative generalized HP filters that are applicable for this purpose. We provide their properties and a way of specifying those smoothing parameters that are required for their application. In addition, we numerically examine their performance. Finally, based on our analysis, we recommend one of them for applied studies.

中文翻译：

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通用霍德里克-普雷斯科特过滤器从经济时间序列中提取缺少观测值的趋势

Hodrick-Prescott (HP) 过滤器一直是从经济时间序列中提取趋势的流行方法。但是，如果某些观察结果不可用，则不进行修改是不切实际的。本文对 HP 过滤器进行了改进，使其可以应用于此类情况。更准确地说，本文介绍了适用于此目的的两种替代通用 HP 滤波器。我们提供了它们的属性和指定应用所需的平滑参数的方法。此外，我们对它们的性能进行了数值检查。最后，根据我们的分析，我们推荐其中之一进行应用研究。