Using stochastic volatility models to analyse weekly ozone averages in Mexico City

Achcar, Jorge A.; Rodrigues, Eliane R.; Tzintzun, Guadalupe

doi:10.1007/s10651-010-0132-1

Cited by 12 publications

(18 citation statements)

References 38 publications

(33 reference statements)

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“…We seek to learn whether a heterogeneous variance specification is more appropriate. Although elaborate stochastic volatility models have been developed in past work (Achar, Rodrigues, & Tzintzun, ; Fahrmeir, Kneib, & Lang, ), we only consider simple implementations of heterogeneous variance here, again with focus on real‐time forecasting.…”

Section: Modeling Ideasmentioning

confidence: 99%

Local real‐time forecasting of ozone exposure using temperature data

Gelfand

Holland

2018

Environmetrics

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Rigorous and rapid assessment of ambient ozone exposure is important for informing the public about ozone levels that may lead to adverse health effects. In this paper, we use hierarchical modeling to enable real‐time forecasting of 8‐hr average ozone exposure. This contrasts with customary retrospective analysis of exposure data. Specifically, our contribution is to show how incorporating temperature data in addition to the observed ozone can significantly improve forecast accuracy, as measured by predictive performance and empirical coverage. We adopt two‐stage autoregressive models, also introducing periodicity and heterogeneity while still maintaining our objective of forecasting in real time. The entire effort is illustrated through modeling data collected at the Village Green monitoring station in Durham, North Carolina.

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Section: Modeling Ideasmentioning

confidence: 99%

Local real‐time forecasting of ozone exposure using temperature data

Gelfand

Holland

2018

Environmetrics

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“…Depending on the type of questions that one is trying to answer, different methodologies may be used. Among the many works concentrating on the study of ozone behaviour are, [11][12][13] using extreme value theory to study the behaviour of the maximum ozone measurements; [14] using time series analysis; [15] using volatility models to study the variability of the weekly average ozone measurements; [13,16] using homogeneous Poisson processes and [17,18] using non-homogeneous Poisson models to analyse the probability of having a certain number of ozone exceedances in a time interval of interest; [19] using compound Poisson models to study the occurrence of clusters of ozone exceedances as well as their mean duration time; and [20] using queueing model to study the occurrence of cluster of ozone exceedances as well as their size distribution.…”

Section: Introductionmentioning

confidence: 99%

A Non-Homogeneous Markov Chain Model to Study Ozone Exceedances in Mexico City

Rodrigues¹,

Tarumoto²,

Tzintzun³

2015

Current Air Quality Issues

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Additional information is available at the end of the chapter IntroductionIn many cities around the world, air pollution is among the many environmental problems that affect their population. Among the many known facts about the impact of pollution on human health, we have that for ozone concentration levels above 0.11 parts per million (0.11ppm), the susceptible part of the population (e.g., the elderly, ill, and newborn) staying in that environment for a long period of time, may experience serious health deterioration (see, for example, [1][2][3][4][5][6][7][8][9][10]). Therefore, to understand the behaviour of ozone and/or pollutants in general, is a very important issue.It is possible to find in the literature a vast amount of works that try to answer some of the many issues arising in the study of pollutants' behaviour. Depending on the type of questions that one is trying to answer, different methodologies may be used. Among the many works concentrating on the study of ozone behaviour are, [11][12][13] using extreme value theory to study the behaviour of the maximum ozone measurements; [14] using time series analysis; [15] using volatility models to study the variability of the weekly average ozone measurements; [13,16] using homogeneous Poisson processes and [17, 18] using non-homogeneous Poisson models to analyse the probability of having a certain number of ozone exceedances in a time interval of interest; [19] using compound Poisson models to study the occurrence of clusters of ozone exceedances as well as their mean duration time; and [20] using queueing model to study the occurrence of cluster of ozone exceedances as well as their size distribution.In the environmental area, it is also possible to find works using Markov chains models. Some of them are, [21,22] where non-homogeneous Markov models are used to study the occurrence of precipitation. We also have [23] where those types of models are used to study tornado activity. In the case of ozone modelling we have, for instance, the works of [24][25][26] using time homogeneous Markov chains. In those works the interest was in estimating the probability that the ozone measurement would be above (below) a given threshold, conditioned on where it lays in the present and in the past days.© 2015 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.In [24], the order of the Markov chain was estimated using auto-correlation function. Its transition matrix was estimated using the maximum likelihood method (see, for instance, [27,28], among others). In [25], the order of the chain was also considered an unknown quantity that needed to be estimated. The Bayesian approach (see, for example, [29]) was used to estimate the order as well as the transition probabilities of the chain. In particular, the maximum à posteriori method wa...

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“…It is possible to find in the literature a large number of works focussing on the study of the behaviour of air pollutants in general. Among the ones related to ozone air pollution we may quote, Horowitz (1980), Roberts (1979aRoberts ( , 1979b, Smith (1989) considering extreme value theory; Flaum et al (1996), Gouveia & Fletcher (2000), Kumar et al (2010), Lanfredi & Macchiato (1997) and Pan & Chen (2008) using time series analysis; Álvarez et al (2005) and Austin & Tran (1999) considering Markov chain models; Achcar et al (2008bAchcar et al ( , 2009aAchcar et al ( , 2009b using stochastic volatility models; and Huerta & Sansó (2005) with an analysis of the behaviour the maximum measurements of ozone with an application to the data from Mexico City. Davis (2008) and Zavala et al (2009) present studies that analyse the impact on air quality of the driving restriction imposed in Mexico City.…”

Section: Introductionmentioning

confidence: 99%