We address the problem of estimating smoothly varying baseline trends in time series data. This problem arises in a wide range of fields, including chemistry, macroeconomics and medicine; however, our study is motivated by the analysis of data from low cost air quality sensors. Our methods extend the quantile trend filtering framework to enable the estimation of multiple quantile trends simultaneously while ensuring that the quantiles do not cross. To handle the computational challenge posed by very long time series, we propose a parallelizable alternating direction method of multipliers (ADMM) algorithm. The ADMM algorthim enables the estimation of trends in a piecewise manner, both reducing the computation time and extending the limits of the method to larger data sizes. We also address smoothing parameter selection and propose a modified criterion based on the extended Bayesian information criterion. Through simulation studies and our motivating application to low cost air quality sensor data, we demonstrate that our model provides better quantile trend estimates than existing methods and improves signal classification of low-cost air quality sensor output.

中文翻译：

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使用分位数趋势过滤对空气质量数据进行基线漂移估计

我们解决了估计时间序列数据中平稳变化的基线趋势的问题。这个问题在化学，宏观经济学和医学等许多领域都出现。然而，我们的研究是基于对低成本空气质量传感器数据的分析。我们的方法扩展了分位数趋势过滤框架，可以同时估计多个分位数趋势，同时确保分位数不会交叉。为了应对非常长的时间序列带来的计算难题，我们提出了一种可并行化的乘数交替方向方法（ADMM）算法。ADMM算法可以分段估计趋势，既可以减少计算时间，又可以将方法的限制扩展到更大的数据大小。我们还将解决平滑参数选择问题，并基于扩展贝叶斯信息准则提出一种修改准则。通过仿真研究和我们对低成本空气质量传感器数据的积极应用，我们证明了我们的模型比现有方法提供了更好的分位数趋势估计，并改善了低成本空气质量传感器输出的信号分类。