Applied and Computational Mathematics

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Comparison of ARIMA Model and Exponential Smoothing Model on 2014 Air Quality Index in Yanqing County, Beijing, China

Received: 01 November 2015    Accepted: 09 November 2015    Published: 19 November 2015
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Abstract

In order to study the changes of air quality index (AQI) in Yanqing County, Beijing, China and predict the trend of AQI value, this paper constructed a time-series analysis.A non-stationary trend is found, and the ARIMA (1, 1, 2) model and Holt exponential smoothing model are found to sufficiently model the data. In comparison of these two model fittings, the ARIMA modelling result are better than Holt modelling’s in terms of trend capturing and result MSE, and in this data it is better to apply the ARIMA model to predict the future AQI values.

DOI 10.11648/j.acm.20150406.19
Published in Applied and Computational Mathematics (Volume 4, Issue 6, December 2015)
Page(s) 456-461
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Air Quality Index (AQI), Prediction, ARIMA Model, Exponential Smoothing Model, Holt Model

References
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[2] "People's Republic of China Ministry of Environmental Protection Standard: Technical Regulation on Ambient Air Quality Index".
[3] Access:http://kjs.mep.gov.cn/hjbhbz/bzwb/dqhjbh/jcgfffbz/201203/W020120410332725219541.pdf
[4] Box, G.E.P., Jenkins, G.M., and Reinsel, G.C.(1994), Time Series Analysis: Forecasting and Control, 3rd edition, Prentice Hall: Englewood Cliffs, New Jersey.
[5] Box, G.E.P., and Pierce, D. (1970), “Distribution of Residual Autocorrelations in Auto-regressive-Intergrated Moving Average Time Series Models,” Journal of the American statistical Association, 65, 1509-1526.
[6] Anders Milhoj (2013). Practical Time Series Analysis Using SAS. NC: SAS Institute Inc, Cary.
[7] SAS Institute Inc, (2014). SAS/STAT® 9.4 User’s Guide: The ARIMA Procedure (Book Excerpt). NC: SAS Institute Inc, Cary.
[8] SAS Institute Inc, (2014). SAS/STAT® 9.4 User’s Guide: The ESM Procedure (Book Excerpt). NC: SAS Institute Inc, Cary.
[9] Bollerslev T. Generalized autoregressive conditional heteroskedasticity [J]. Journal of Econometrics, 1986, 31 (3): 309-317.
[10] Engle R.F. Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation [J]. Econometric, 1982, 50 (4): 989-1004.
[11] Engle R.F., Kroner F.K. Multivariate Simultaneous Generalized ARCH [J]. Econometric Theory, 1995, 11: 135-149.
[12] Tsay, R.S., and Tiao, G.C. (1984), “Consistent Estimates of Auto-regressive Parameters and Extended Sample Auto-correlation Function for Stationary and Non-stationary ARMA models,” Journal of American Statistical Association, 79, 84-96.
[13] Cox, D. R., & Wermuth, N. (1991). A simple approximation for bivariate and trivariate normal integrals. International Statistical Review/Revue Internationale de Statistique, 59(2), 263-269.
[14] Engle Robert F. Dynamic Conditional Correlation: A Simple Class of Multivariate GARCH Models [J]. Journal of Business and Economic Statistics, 2002, 20 (3): 341-347.
[15] Engle R.F., Lilien D.M., Robins R.P. Estimating time-varying risk Premia in the term structure: The ARCH-M model [J]. Econometrica, 1987, 55: 395-406.
[16] Akaike, H. (1973), “Information Theory and an Extension of the Maximum Likelihood Principle,” in B.N. Petrov and F. Csaki, ed. 2nd International Symposium on Information Theory, 267-281. Akademia Kiado: Budapest.
Author Information
  • School of Information, Beijing Wuzi University, Beijing, China

  • School of Information, Beijing Wuzi University, Beijing, China

  • School of Information, Beijing Wuzi University, Beijing, China

  • School of Information, Beijing Wuzi University, Beijing, China

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  • APA Style

    Jie Zhu, Ruoling Zhang, Binbin Fu, Renhao Jin. (2015). Comparison of ARIMA Model and Exponential Smoothing Model on 2014 Air Quality Index in Yanqing County, Beijing, China. Applied and Computational Mathematics, 4(6), 456-461. https://doi.org/10.11648/j.acm.20150406.19

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    ACS Style

    Jie Zhu; Ruoling Zhang; Binbin Fu; Renhao Jin. Comparison of ARIMA Model and Exponential Smoothing Model on 2014 Air Quality Index in Yanqing County, Beijing, China. Appl. Comput. Math. 2015, 4(6), 456-461. doi: 10.11648/j.acm.20150406.19

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    AMA Style

    Jie Zhu, Ruoling Zhang, Binbin Fu, Renhao Jin. Comparison of ARIMA Model and Exponential Smoothing Model on 2014 Air Quality Index in Yanqing County, Beijing, China. Appl Comput Math. 2015;4(6):456-461. doi: 10.11648/j.acm.20150406.19

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  • @article{10.11648/j.acm.20150406.19,
      author = {Jie Zhu and Ruoling Zhang and Binbin Fu and Renhao Jin},
      title = {Comparison of ARIMA Model and Exponential Smoothing Model on 2014 Air Quality Index in Yanqing County, Beijing, China},
      journal = {Applied and Computational Mathematics},
      volume = {4},
      number = {6},
      pages = {456-461},
      doi = {10.11648/j.acm.20150406.19},
      url = {https://doi.org/10.11648/j.acm.20150406.19},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.acm.20150406.19},
      abstract = {In order to study the changes of air quality index (AQI) in Yanqing County, Beijing, China and predict the trend of AQI value, this paper constructed a time-series analysis.A non-stationary trend is found, and the ARIMA (1, 1, 2) model and Holt exponential smoothing model are found to sufficiently model the data. In comparison of these two model fittings, the ARIMA modelling result are better than Holt modelling’s in terms of trend capturing and result MSE, and in this data it is better to apply the ARIMA model to predict the future AQI values.},
     year = {2015}
    }
    

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    AB  - In order to study the changes of air quality index (AQI) in Yanqing County, Beijing, China and predict the trend of AQI value, this paper constructed a time-series analysis.A non-stationary trend is found, and the ARIMA (1, 1, 2) model and Holt exponential smoothing model are found to sufficiently model the data. In comparison of these two model fittings, the ARIMA modelling result are better than Holt modelling’s in terms of trend capturing and result MSE, and in this data it is better to apply the ARIMA model to predict the future AQI values.
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