IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i13p2280-d851571.html
   My bibliography  Save this article

Bayesian Information Criterion for Fitting the Optimum Order of Markov Chain Models: Methodology and Application to Air Pollution Data

Author

Listed:
  • Yousif Alyousifi

    (Department of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia, Serdang 43400, Selangor, Malaysia
    Department of Mathematics, Faculty of Applied Science, Thamar University, Dhamar 00967, Yemen)

  • Kamarulzaman Ibrahim

    (Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600, Selangor, Malaysia)

  • Mahmod Othamn

    (Fundamental and Applied Sciences Department, Universiti Teknologi PETRONAS, Seri Iskandar 32160, Perak, Malaysia)

  • Wan Zawiah Wan Zin

    (Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600, Selangor, Malaysia)

  • Nicolas Vergne

    (CNRS, Laboratoire de Mathématiques Raphaël Salem, Normandie University, UNIROUEN, 76000 Rouen, France)

  • Abdullah Al-Yaari

    (Department of Mathematics, Faculty of Applied Science, Thamar University, Dhamar 00967, Yemen
    Fundamental and Applied Sciences Department, Universiti Teknologi PETRONAS, Seri Iskandar 32160, Perak, Malaysia)

Abstract

The analysis of air pollution behavior is becoming crucial, where information on air pollution behavior is vital for managing air quality events. Many studies have described the stochastic behavior of air pollution based on the Markov chain (MC) models. Fitting the optimum order of MC models is essential for describing the stochastic process. However, uncertainty remains concerning the optimum order of such models for representing and characterizing air pollution index (API) data. In this study, the optimum order of the MC models for hourly and daily API sequences from seven stations in the central region of Peninsular Malaysia is identified, based on the Bayesian information criteria (BIC), contributing to exploring an adequate explanation of the probabilistic dependence of air pollution. A summary of the statistics for the API was calculated prior to the analysis. The Markov property and the divergence for the empirically estimated transition matrix of an MC sequence are also investigated. It is found from the analysis that the optimum order varies from one station to another. At most stations, for both observed and simulated API data, the second and third orders of the MC models are found to be optimum for hourly API occurrences, while the first-order MC is found to be most fitting for describing the dynamics of the daily API. Overall, fitting the optimum order of the MC model for the API data sequence captured the delay effect of air pollution. Accordingly, we concluded that the air quality standard lies within controllable limits, except for some infrequent occurrences of API values exceeding the unhealthy level.

Suggested Citation

  • Yousif Alyousifi & Kamarulzaman Ibrahim & Mahmod Othamn & Wan Zawiah Wan Zin & Nicolas Vergne & Abdullah Al-Yaari, 2022. "Bayesian Information Criterion for Fitting the Optimum Order of Markov Chain Models: Methodology and Application to Air Pollution Data," Mathematics, MDPI, vol. 10(13), pages 1-16, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:13:p:2280-:d:851571
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/13/2280/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/13/2280/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Bickenbach, Frank & Bode, Eckhardt, 2001. "Markov or not Markov - this should be a question," Kiel Working Papers 1086, Kiel Institute for the World Economy (IfW Kiel).
    2. Rodrigo Puentes & Carolina Marchant & Víctor Leiva & Jorge I. Figueroa-Zúñiga & Fabrizio Ruggeri, 2021. "Predicting PM2.5 and PM10 Levels during Critical Episodes Management in Santiago, Chile, with a Bivariate Birnbaum-Saunders Log-Linear Model," Mathematics, MDPI, vol. 9(6), pages 1-24, March.
    3. Frank Bickenbach & Eckhardt Bode, 2003. "Evaluating the Markov Property in Studies of Economic Convergence," International Regional Science Review, , vol. 26(3), pages 363-392, July.
    4. Carlos Salas-Páez & Luis Quintana-Romero & Miguel A. Mendoza-González & José Álvarez-García, 2022. "Analysis of Job Transitions in Mexico with Markov Chains in Discrete Time," Mathematics, MDPI, vol. 10(10), pages 1-13, May.
    5. Wai-Ki Ching & Ximin Huang & Michael K. Ng & Tak-Kuen Siu, 2013. "Higher-Order Markov Chains," International Series in Operations Research & Management Science, in: Markov Chains, edition 2, chapter 0, pages 141-176, Springer.
    6. Yajun Zhou & Lilei Wang & Rong Zhong & Yulong Tan, 2018. "A Markov Chain Based Demand Prediction Model for Stations in Bike Sharing Systems," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-8, January.
    7. Vlad Stefan Barbu & Nicolas Vergne, 2019. "Reliability and Survival Analysis for Drifting Markov Models: Modeling and Estimation," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1407-1429, December.
    8. Shamshad, A. & Bawadi, M.A. & Wan Hussin, W.M.A. & Majid, T.A. & Sanusi, S.A.M., 2005. "First and second order Markov chain models for synthetic generation of wind speed time series," Energy, Elsevier, vol. 30(5), pages 693-708.
    9. Vergne Nicolas, 2008. "Drifting Markov Models with Polynomial Drift and Applications to DNA Sequences," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 7(1), pages 1-45, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Monica Aureliana Petcu & Liliana Ionescu-Feleaga & Bogdan-Ștefan Ionescu & Dumitru-Florin Moise, 2023. "A Decade for the Mathematics : Bibliometric Analysis of Mathematical Modeling in Economics, Ecology, and Environment," Mathematics, MDPI, vol. 11(2), pages 1-30, January.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Nilsson, Isabelle & Delmelle, Elizabeth, 2018. "Transit investments and neighborhood change: On the likelihood of change," Journal of Transport Geography, Elsevier, vol. 66(C), pages 167-179.
    2. Eckey, Hans-Friedrich & Türck, Matthias, 2005. "Convergence of EU-regions: A literature report," Volkswirtschaftliche Diskussionsbeiträge 80, University of Kassel, Faculty of Economics and Management.
    3. Eckey, Hans-Friedrich & Türck, Matthias, 2007. "Convergence of EU-Regions. A Literature Report," INVESTIGACIONES REGIONALES - Journal of REGIONAL RESEARCH, Asociación Española de Ciencia Regional, issue 10, pages 5-32.
    4. Mariano Bosch Mossi & Patricio Aroca & Ismael J. FernáNDEZ & Carlos Roberto Azzoni, 2003. "Growth Dynamics and Space in Brazil," International Regional Science Review, , vol. 26(3), pages 393-418, July.
    5. Henryk Gurgul & Łukasz Lach, 2019. "Regional patterns in technological progress of Poland: the role of EU structural funds," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 27(4), pages 1195-1220, December.
    6. Sergio J. Rey & Mark V. Janikas, 2003. "Convergence and space," Urban/Regional 0311002, University Library of Munich, Germany, revised 16 Nov 2003.
    7. Sergio J. Rey & Mark V. Janikas, 2005. "Regional convergence, inequality, and space," Journal of Economic Geography, Oxford University Press, vol. 5(2), pages 155-176, April.
    8. Rey, Sergio, 2015. "Bells in Space: The Spatial Dynamics of US Interpersonal and Interregional Income Inequality," MPRA Paper 69482, University Library of Munich, Germany.
    9. María Hierro & Adolfo Maza, 2015. "From Discrete To Continuous-Time Transition Matrices In Intra-Distribution Dynamics Analysis: An Application To Per Capita Wealth In Europe," Bulletin of Economic Research, Wiley Blackwell, vol. 67(3), pages 227-235, July.
    10. Jørn Rattsø & Hildegunn E. Stokke, 2011. "Accumulation of education and regional income growth: Limited human capital effects in Norway," Working Paper Series 11211, Department of Economics, Norwegian University of Science and Technology.
    11. Hong, Ying-Yi & Chang, Huei-Lin & Chiu, Ching-Sheng, 2010. "Hour-ahead wind power and speed forecasting using simultaneous perturbation stochastic approximation (SPSA) algorithm and neural network with fuzzy inputs," Energy, Elsevier, vol. 35(9), pages 3870-3876.
    12. Sébastien Massoni & Madalina Olteanu & Patrick Rousset, 2010. "Career-path analysis using drifting Markov models (DMM) and self-organizing maps," Post-Print hal-00443530, HAL.
    13. Amanda S. Hering & Karen Kazor & William Kleiber, 2015. "A Markov-Switching Vector Autoregressive Stochastic Wind Generator for Multiple Spatial and Temporal Scales," Resources, MDPI, vol. 4(1), pages 1-23, February.
    14. repec:diw:diwfin:diwfin01050 is not listed on IDEAS
    15. Zhang, Jin-hua & Liu, Yong-qian & Tian, De & Yan, Jie, 2015. "Optimal power dispatch in wind farm based on reduced blade damage and generator losses," Renewable and Sustainable Energy Reviews, Elsevier, vol. 44(C), pages 64-77.
    16. Maarten Bosker & Waldo Krugell, 2008. "Regional Income Evolution In South Africa After Apartheid," Journal of Regional Science, Wiley Blackwell, vol. 48(3), pages 493-523, August.
    17. Eckhardt Bode & Peter Nunnenkamp, 2011. "Does foreign direct investment promote regional development in developed countries? A Markov chain approach for US states," Review of World Economics (Weltwirtschaftliches Archiv), Springer;Institut für Weltwirtschaft (Kiel Institute for the World Economy), vol. 147(2), pages 351-383, June.
    18. Santiago Rodriguez Feijoo & Alejandro Rodriguez Caro & Carlos Gonzalez Correa, 2004. "An Empirical Study of the Purchasing Power Parity in the European Union," ERSA conference papers ersa04p369, European Regional Science Association.
    19. Cheong, Tsun Se & Wu, Yanrui, 2013. "Regional disparity, transitional dynamics and convergence in China," Journal of Asian Economics, Elsevier, vol. 29(C), pages 1-14.
    20. D׳Amico, Guglielmo & Petroni, Filippo & Prattico, Flavio, 2015. "Reliability measures for indexed semi-Markov chains applied to wind energy production," Reliability Engineering and System Safety, Elsevier, vol. 144(C), pages 170-177.
    21. Andrés Vallone & Coro Chasco, 2020. "Spatiotemporal methods for analysis of urban system dynamics: an application to Chile," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 64(2), pages 421-454, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:13:p:2280-:d:851571. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.