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Statistical Inference of Dynamic Conditional Generalized Pareto Distribution with Weather and Air Quality Factors

Author

Listed:
  • Chunli Huang

    (Faculty of Science, Beijing University of Technology, Beijing 100124, China)

  • Xu Zhao

    (Faculty of Science, Beijing University of Technology, Beijing 100124, China)

  • Weihu Cheng

    (Faculty of Science, Beijing University of Technology, Beijing 100124, China)

  • Qingqing Ji

    (University of Chinese Academy of Sciences, Beijing 100049, China
    Institute of Computing Technology, Chinese Academy of Sciences, Beijing 100190, China)

  • Qiao Duan

    (Faculty of Humanities and Social Sciences, Beijing University of Technology, Beijing 100124, China)

  • Yufei Han

    (School of Computer Science (National Pilot Software Engineering School), Beijing University of Posts and Telecommunications, Beijing 100876, China)

Abstract

Air pollution is a major global problem, closely related to economic and social development and ecological environment construction. Air pollution data for most regions of China have a close correlation with time and seasons and are affected by multidimensional factors such as meteorology and air quality. In contrast with classical peaks-over-threshold modeling approaches, we use a deep learning technique and three new dynamic conditional generalized Pareto distribution (DCP) models with weather and air quality factors for fitting the time-dependence of the air pollutant concentration and make statistical inferences about their application in air quality analysis. Specifically, in the proposed three DCP models, a dynamic autoregressive exponential function mechanism is applied for the time-varying scale parameter and tail index of the conditional generalized Pareto distribution, and a sufficiently high threshold is chosen using two threshold selection procedures. The probabilistic properties of the DCP model and the statistical properties of the maximum likelihood estimation (MLE) are investigated, simulating and showing the stability and sensitivity of the MLE estimations. The three proposed models are applied to fit the PM 2.5 time series in Beijing from 2015 to 2021. Real data are used to illustrate the advantages of the DCP, especially compared to the estimation volatility of GARCH and AIC or BIC criteria. The DCP model involving both the mixed weather and air quality factors performs better than the other two models with weather factors or air quality factors alone. Finally, a prediction model based on long short-term memory (LSTM) is used to predict PM 2.5 concentration, achieving ideal results.

Suggested Citation

  • Chunli Huang & Xu Zhao & Weihu Cheng & Qingqing Ji & Qiao Duan & Yufei Han, 2022. "Statistical Inference of Dynamic Conditional Generalized Pareto Distribution with Weather and Air Quality Factors," Mathematics, MDPI, vol. 10(9), pages 1-25, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:9:p:1433-:d:800987
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    References listed on IDEAS

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    Cited by:

    1. Julia Adamska & Łukasz Bielak & Joanna Janczura & Agnieszka Wyłomańska, 2022. "From Multi- to Univariate: A Product Random Variable with an Application to Electricity Market Transactions: Pareto and Student’s t -Distribution Case," Mathematics, MDPI, vol. 10(18), pages 1-29, September.
    2. Nurulkamal Masseran, 2022. "Multifractal Characteristics on Temporal Maximum of Air Pollution Series," Mathematics, MDPI, vol. 10(20), pages 1-15, October.

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