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Fulltext A new hybrid fuzzy time series model with an application to predict PM10 concentration

Alyousifi Y, Othman M, Husin A, Rathnayake U

Ecotoxicol Environ Saf, 2021 Dec 20;227:112875.
PMID: 34717219 DOI: 10.1016/j.ecoenv.2021.112875

Fuzzy time series (FTS) forecasting models show a great performance in predicting time series, such as air pollution time series. However, they have caused major issues by utilizing random partitioning of the universe of discourse and ignoring repeated fuzzy sets. In this study, a novel hybrid forecasting model by integrating fuzzy time series to Markov chain and C-Means clustering techniques with an optimal number of clusters is presented. This hybridization contributes to generating effective lengths of intervals and thus, improving the model accuracy. The proposed model was verified and validated with real time series data sets, which are the benchmark data of actual trading of Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) and PM10 concentration data from Melaka, Malaysia. In addition, a comparison was made with some existing fuzzy time series models. Furthermore, the mean absolute percentage error, mean squared error and Theil's U statistic were calculated as evaluation criteria to illustrate the performance of the proposed model. The empirical analysis shows that the proposed model handles the time series data sets more efficiently and provides better overall forecasting results than existing FTS models. The results prove that the proposed model has greatly improved the prediction accuracy, for which it outperforms several fuzzy time series models. Therefore, it can be concluded that the proposed model is a better option for forecasting air pollution parameters and any kind of random parameters.
Modeling the spatio-temporal dynamics of air pollution index based on spatial Markov chain model

Alyousifi Y, Ibrahim K, Kang W, Zin WZW

Environ Monit Assess, 2020 Oct 21;192(11):719.
PMID: 33083907 DOI: 10.1007/s10661-020-08666-8

An environmental problem which is of concern across the globe nowadays is air pollution. The extent of air pollution is often studied based on data on the observed level of air pollution. Although the analysis of air pollution data that is available in the literature is numerous, studies on the dynamics of air pollution with the allowance for spatial interaction effects through the use of the Markov chain model are very limited. Accordingly, this study aims to explore the potential impact of spatial dependence over time and space on the distribution of air pollution based on the spatial Markov chain (SMC) model using the longitudinal air pollution index (API) data. This SMC model is pertinent to be applied since the daily data of API from 2012 to 2014 that have been gathered from 37 different air quality stations in Peninsular Malaysia is found to exhibit the property of spatial autocorrelation. Based on the spatial transition probability matrices found from the SMC model, specific characteristics of air pollution are studied in the regional context. These characteristics are the long-run proportion and the mean first passage time for each state of air pollution. It is found that the probability for a particular station's state to remain good is 0.814 if its neighbors are in a good state of air pollution and 0.7082 if its neighbors are in a moderate state. For a particular station having neighbors in a good state of air pollution, the proportion of time for it to continue being in a good state is 0.6. This proportion reduces to 0.4, 0.01, and 0 for the cell of moderate, unhealthy, and very unhealthy states, respectively. In addition, there exists a significant spatial dependence of API, indicating that air pollution for a particular station is dependent on the states of the neighboring stations.
Correction to: Modeling the spatio-temporal dynamics of air pollution index based on spatial Markov chain model

Alyousifi Y, Ibrahim K, Kang W, Zin WZW

Environ Monit Assess, 2020 Nov 08;192(12):753.
PMID: 33164139 DOI: 10.1007/s10661-020-08720-5

The original version of this article unfortunately contained an error in the affiliation section and in the main body text.
Fulltext Robust empirical Bayes approach for Markov chain modeling of air pollution index

Alyousifi Y, Ibrahim K, Kang W, Zin WZW

J Environ Health Sci Eng, 2021 Jun;19(1):343-356.
PMID: 34150239 DOI: 10.1007/s40201-020-00607-4

Air pollution is a matter of concern among the public, especially for those living in urban and industrial areas. Markov chain modeling is often used to model the underlying dynamics of air pollution, which involves describing the transition probability of going from one air pollution state to another. Thus, estimating the transition probability matrix for the data of the air pollution index (API) is an essential process in the modeling. However, one may observe many zero probabilities in the transition probability matrix, especially when faced with a small sample, interpreting the results with respect to the climate condition less realistic. This study proposes a robust empirical Bayes method, which incorporates a method of smoothing the zero frequencies in the count matrix, contributing to an improved estimation of the transition probability matrix. The robustness of the empirical Bayesian estimation is investigated based on Bayes risk. The transition probability matrices estimated based on the robust empirical Bayes method for the hourly API data collected from seven monitoring stations in Malaysia for the period 2012 to 2014 are used for determining the air pollution characteristics such as the mean residence time, the steady-state probability and the mean recurrence time. Furthermore, the proposed method has been evaluated by Monte Carlo simulations. Results suggest that it is quite effective in producing non-zero transition probability estimates, and superior to the maximum likelihood method in terms of minimizing the mean squared error for individual and entire transition probabilities. Therefore, the robust empirical Bayes method proves to be an improved approach to the estimation of the Markov chain. When applied to API data, it could provide important information on air pollution dynamics that may help guiding the development of proper strategies for managing the impact of air quality.
Supplementary Information: The online version contains supplementary material available at 10.1007/s40201-020-00607-4.