Abstract
In recent years, air pollution has been a major concern for its implications on human health. Specifically, ozone (mathrm{O}_{3}) pollution is causing common respiratory diseases. In this paper, we illustrate the process of modeling and prediction hourly mathrm{O}_ {3} pollution measurements using wavelet transforms. We split the time series of mathrm{O}_{3} 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.
Highlights
The atmospheric pollution is a great concern for many countries of the world, as a result of studies that have verified the negative effects on human health
In order to assess the performance of the proposed methodology, we compare the predictions obtained by the discrete wavelet transform (DWT)–autoregressive integrated moving average (ARIMA) with those obtained by the ARIMA model
We propose a new methodology for predicting the ozone concentrations in Santiago de Chile given by the combination of the wavelet analysis with the accumulated ARIMA approach
Summary
The atmospheric pollution is a great concern for many countries of the world, as a result of studies that have verified the negative effects on human health. We propose a new methodology for predicting the ozone concentrations in Santiago de Chile given by the combination of the wavelet analysis with the accumulated ARIMA approach. Soltani [12] proposed to combine the wavelet approach with the artificial neural networks (ANN) for predicting the sun spot and MacKey–Glass time series. Mabrouk et al [13] used the autoregressive models and the wavelet decomposition for forecasting the sun spot time series The idea of the latter works is to predict time series by applying linear (ARMAX) or nonlinear (ANN) models on simplified signal given by the reconstructed time series in each level of resolution. From the point of view of this approach, our work is novel since we propose to apply linear models to the scaling and wavelet coefficients obtained by the discrete wavelet decomposition using the wavelet Haar filter.
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