Trend filtering is a regression problem to estimate underlying trends in time series data. It is necessary to investigate data in various disciplines. We propose a trend filtering method by adaptive piecewise polynomials. More specifically, we adjust the location and the number of breakpoints or knots to obtain a better fitting to given data. The numerical results on synthetic and real data sets show that it captures distinct features such as abrupt changes or kinks and provides a simplified form and brief summary of given data.

中文翻译：

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通过自适应分段多项式进行趋势过滤

趋势过滤是一个回归问题，用于估计时间序列数据中的潜在趋势。有必要调查各个学科的数据。我们提出了一种自适应分段多项式的趋势过滤方法。更具体地说，我们调整断点或节点的位置和数量，以获得对给定数据的更好拟合。合成数据集和真实数据集的数值结果表明，它捕获了诸如突然变化或扭结等不同的特征，并提供了给定数据的简化形式和简要摘要。