Detecting time-changes in $ PM_{10} $ during Covid pandemic by means of an Ornstein Uhlenbeck type process

Giuseppina Albano; Giuseppina Albano

doi:10.3934/mbe.2021047

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 1: 888-903. doi: 10.3934/mbe.2021047

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Detecting time-changes in $ PM_{10} $ during Covid pandemic by means of an Ornstein Uhlenbeck type process

Giuseppina Albano ^,

Dipartimento di Studi Politici e Sociali, Università degli Studi di Salerno, Via Giovanni Paolo II, 84084 Fisciano (SA), Italy

Received: 05 October 2020 Accepted: 13 December 2020 Published: 31 December 2020

Particulate matter with 10 micrometers or less in diameter ($ PM_{10} $) from several italian cities is modeled by means of a non homogeneous Ornstein Uhlenbeck process. Such model includes two deterministic time dependent functions in the infinitesimal moments to describe the presence of exogeneous terms in the typical dynamics of the phenomenon. An iterative estimating procedure combining the maximum likelihood estimation and a generalized method of moments is provided. A Quandt Likelihood Ratio test for detecting structural breaks in $ PM_{10} $ data, in the period from 1st January 2020 to 8th July 2020 which includes the first lockdown due to Covid pandemic, confirms the presence of time-changes. These results show that the lockdown made the air once again cleaner. It is then shown that our model and the associated estimation procedure, while not explicitly contemplating the presence of structural breaks in the time series, implicitly incorporates them in the time dependence of the functions in the infinitesimal moments of the underlying process.
- non homogeneous Ornstein Uhlenbeck processes,
- estimating procedure,
- $ PM_{10} $,
- structural breaks
Citation: Giuseppina Albano. Detecting time-changes in $ PM_{10} $ during Covid pandemic by means of an Ornstein Uhlenbeck type process[J]. Mathematical Biosciences and Engineering, 2021, 18(1): 888-903. doi: 10.3934/mbe.2021047

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Abstract

Particulate matter with 10 micrometers or less in diameter ($ PM_{10} $) from several italian cities is modeled by means of a non homogeneous Ornstein Uhlenbeck process. Such model includes two deterministic time dependent functions in the infinitesimal moments to describe the presence of exogeneous terms in the typical dynamics of the phenomenon. An iterative estimating procedure combining the maximum likelihood estimation and a generalized method of moments is provided. A Quandt Likelihood Ratio test for detecting structural breaks in $ PM_{10} $ data, in the period from 1st January 2020 to 8th July 2020 which includes the first lockdown due to Covid pandemic, confirms the presence of time-changes. These results show that the lockdown made the air once again cleaner. It is then shown that our model and the associated estimation procedure, while not explicitly contemplating the presence of structural breaks in the time series, implicitly incorporates them in the time dependence of the functions in the infinitesimal moments of the underlying process.

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