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June 2020 Baseline drift estimation for air quality data using quantile trend filtering
Halley L. Brantley, Joseph Guinness, Eric C. Chi
Ann. Appl. Stat. 14(2): 585-604 (June 2020). DOI: 10.1214/19-AOAS1318


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.


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Halley L. Brantley. Joseph Guinness. Eric C. Chi. "Baseline drift estimation for air quality data using quantile trend filtering." Ann. Appl. Stat. 14 (2) 585 - 604, June 2020.


Received: 1 April 2019; Revised: 1 November 2019; Published: June 2020
First available in Project Euclid: 29 June 2020

zbMATH: 07239875
MathSciNet: MR4117821
Digital Object Identifier: 10.1214/19-AOAS1318

Keywords: Air quality , nonparametric quantile regression , trend estimation

Rights: Copyright © 2020 Institute of Mathematical Statistics


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Vol.14 • No. 2 • June 2020
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