Predicting hourly ozone concentrations using wavelets and ARIMA models

In recent years, air pollution has been a major concern for its implications on human health. Specifically, ozone (O3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{O}_{3}$$\end{document}) pollution is causing common respiratory diseases. In this paper, we illustrate the process of modeling and prediction hourly O3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{O}_ {3}$$\end{document} pollution measurements using wavelet transforms. We split the time series of O3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{O}_{3}$$\end{document} in daily intervals and estimate scale and wavelet coefficients for each interval by the discrete wavelet transform (DWT) with Haar filter. Subsequently we apply cumulated autoregressive integrated moving average (ARIMA) to estimate the coefficients and forecast their evolution in future intervals. Then the inverse discrete wavelet transform is implemented for the reconstruction of the time series and the forecast in the near future. In order to assess the performance of the proposed methodology, we compare the predictions obtained by the DWT–ARIMA with those obtained by the ARIMA model. Several theoretical results are shown through a simulation study.