We propose a procedure of iterating the HP filter to produce a smarter smoothing device, called the boosted HP (bHP) filter, based on L₂-boosting in machine learning. Limit theory shows that the bHP filter asymptotically recovers trend mechanisms that involve integrated processes, deterministic drifts, and structural breaks, covering the most common trends that appear in current modeling methodology. A stopping criterion automates the algorithm, giving a data-determined method for data-rich environments. The methodology is illustrated in simulations and with three real data examples that highlight the differences between simple HP filtering, the bHP filter, and an alternative autoregressive approach.

中文翻译：

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引导：为什么可以使用HP过滤器

基于机器学习中的L ₂提升，我们提出了一个迭代HP过滤器以生成更智能的平滑设备的程序，该设备称为增强HP（bHP）过滤器。极限理论表明，bHP滤波器渐近地恢复了涉及集成过程，确定性漂移和结构断裂的趋势机制，涵盖了当前建模方法中最常见的趋势。停止条件使算法自动化，从而为数据丰富的环境提供了一种数据确定的方法。在仿真中演示了该方法，并通过三个实际数据示例突出了简单的HP过滤，bHP过滤器和另一种自回归方法之间的差异。