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A new autoregressive process driven by explanatory variables and past observations: an application to PM 2.5

Author

Listed:
  • Zheqi Wang

    (Liaoning University
    Jilin University
    Dawning International Information Industry Co., Ltd.)

  • Dehui Wang

    (Liaoning University)

  • Jianhua Cheng

    (Jilin University)

Abstract

This paper uses the empirical likelihood (EL) method for a new random coefficient autoregressive process driven by explanatory variables and past observations through logistic structure (OD-RCAR (1)), which combines explanatory variables and past observations, and puts forward the penalized maximum empirical likelihood (PMEL) method for parameters estimation and variable selection. Firstly, limiting distributions of the estimating function and log empirical likelihood ratio statistics based on EL are established. Meanwhile, this paper sets up a confidence region and EL test for parameters. Secondly, the maximum empirical likelihood estimators and their asymptotic properties are obtained. At the same time, the penalized empirical likelihood ratio test statistic is given. Thirdly, it is proved in a high-dimensional setting that the PMEL in our model can solve the problem of order selection and parameter estimation. Finally, not only practical data applications but also numerical simulations are adopted in order to describe the performance of proposed methods.

Suggested Citation

  • Zheqi Wang & Dehui Wang & Jianhua Cheng, 2023. "A new autoregressive process driven by explanatory variables and past observations: an application to PM 2.5," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(2), pages 619-658, June.
  • Handle: RePEc:spr:stmapp:v:32:y:2023:i:2:d:10.1007_s10260-022-00671-0
    DOI: 10.1007/s10260-022-00671-0
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    References listed on IDEAS

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    1. Chenlei Leng & Cheng Yong Tang, 2012. "Penalized empirical likelihood and growing dimensional general estimating equations," Biometrika, Biometrika Trust, vol. 99(3), pages 703-716.
    2. Hoderlein, Stefan & Klemelä, Jussi & Mammen, Enno, 2010. "Analyzing The Random Coefficient Model Nonparametrically," Econometric Theory, Cambridge University Press, vol. 26(3), pages 804-837, June.
    3. Whitney K. Newey & Richard J. Smith, 2004. "Higher Order Properties of Gmm and Generalized Empirical Likelihood Estimators," Econometrica, Econometric Society, vol. 72(1), pages 219-255, January.
    4. Bang-Qiang He & Xing-Jian Hong & Guo-Liang Fan, 2020. "Penalized empirical likelihood for partially linear errors-in-variables panel data models with fixed effects," Statistical Papers, Springer, vol. 61(6), pages 2351-2381, December.
    5. Joakim Westerlund & Paresh Narayan, 2015. "A Random Coefficient Approach to the Predictability of Stock Returns in Panels," Journal of Financial Econometrics, Oxford University Press, vol. 13(3), pages 605-664.
    6. Stephan Martin, 2022. "Estimation of Conditional Random Coefficient Models using Machine Learning Techniques," Papers 2201.08366, arXiv.org.
    7. Raju Maiti & Atanu Biswas & Bibhas Chakraborty, 2018. "Modelling of low count heavy tailed time series data consisting large number of zeros and ones," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(3), pages 407-435, August.
    8. Xia Chen & Liyue Mao, 2020. "Penalized empirical likelihood for partially linear errors-in-variables models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(4), pages 597-623, December.
    9. Zheng, Haitao & Basawa, Ishwar V., 2008. "First-order observation-driven integer-valued autoregressive processes," Statistics & Probability Letters, Elsevier, vol. 78(1), pages 1-9, January.
    10. Alexander Aue & Lajos Horváth & Josef Steinebach, 2006. "Estimation in Random Coefficient Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(1), pages 61-76, January.
    11. Horváth, Lajos & Trapani, Lorenzo, 2016. "Statistical inference in a random coefficient panel model," Journal of Econometrics, Elsevier, vol. 193(1), pages 54-75.
    12. Cheng Yong Tang & Chenlei Leng, 2010. "Penalized high-dimensional empirical likelihood," Biometrika, Biometrika Trust, vol. 97(4), pages 905-920.
    13. Paul D. Feigin & Richard L. Tweedie, 1985. "Random Coefficient Autoregressive Processes:A Markov Chain Analysis Of Stationarity And Finiteness Of Moments," Journal of Time Series Analysis, Wiley Blackwell, vol. 6(1), pages 1-14, January.
    14. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    15. Horowitz, Joel L. & Nesheim, Lars, 2021. "Using penalized likelihood to select parameters in a random coefficients multinomial logit model," Journal of Econometrics, Elsevier, vol. 222(1), pages 44-55.
    16. Zhang, Ting & Wang, Lei, 2020. "Smoothed empirical likelihood inference and variable selection for quantile regression with nonignorable missing response," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    17. István Berkes & Lajos Horváth & Shiqing Ling, 2009. "Estimation in nonstationary random coefficient autoregressive models," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(4), pages 395-416, July.
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