Impact of Algorithm Selection on Modeling Ozone Pollution: A Perspective on Box and Tiao (1975)

Mihaela Paun,Bogdan M Strimbu,Nevine Gunaime

doi:10.3390/f11121311

Abstract

Estimation using a suboptimal method can lead to imprecise models, with cascading effects in complex models, such as climate change or pollution. The goal of this study is to compare the solutions supplied by different algorithms used to model ozone pollution. Using Box and Tiao (1975) study, we have predicted ozone concentration in Los Angeles with an ARIMA and an autoregressive process. We have solved the ARIMA process with three algorithms (i.e., maximum likelihood, like Box and Tiao, conditional least square and unconditional least square) and the autoregressive process with four algorithms (i.e., Yule–Walker, iterative Yule–Walker, maximum likelihood, and unconditional least square). Our study shows that Box and Tiao chose the appropriate algorithm according to the AIC but not according to the mean square error. Furthermore, Yule–Walker, which is the default algorithm in many software, has the least reliable results, suggesting that the method of solving complex models could alter the findings. Finally, the model selection depends on the technical details and on the applicability of the model, as the ARIMA model is suitable from the AIC perspective but an autoregressive model could be preferred from the mean square error viewpoint. Our study shows that time series analysis should consider not only the model shape but also the model estimation, to ensure valid results.

Highlights

Environmental investigations rely on evidence, which, since the empirical movement ofHume [1] and Locke [2] and the creation of the hypotheses testing by Fisher [3] and Pearson [4], requires formal analyses
Our results confirm the findings of Box and Tiao, as all variables included in the autoregressive integrated moving average (ARIMA) model were significant (p < 0.001), irrespective the algorithm except for the Winter variable, which was significant only for α = 0.1 (Table 2)
We have focused on ozone as pollutant to be modeled, as it is important for forestry and for climate change overall

Summary

Introduction

Environmental investigations rely on evidence, which, since the empirical movement ofHume [1] and Locke [2] and the creation of the hypotheses testing by Fisher [3] and Pearson [4], requires formal analyses. The foundation of most of the analyses are procedures implemented using various software, such as R [5], SAS [6], or Matlab [7]. Numerical algorithms are pivotal in solving any problem involving computations. One problem can be solved with more than one algorithm, but because the aim of most studies is usually to find the solution not the influence of the procedural details, selection of the best algorithm among the available options is customarily ignored. The entrenched approach of data analysis is to use the default options implemented in the software selected for analysis. From a procedural perspective, the significance of studying the impact of different numerical algorithms on the results becomes of major importance. Many studies have been focused on the topic of algorithm impact on the Forests 2020, 11, 1311; doi:10.3390/f11121311 www.mdpi.com/journal/forests

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