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Linear double autoregression

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  • Zhu, Qianqian
  • Zheng, Yao
  • Li, Guodong

Abstract

This paper proposes the linear double autoregression, a conditional heteroscedastic model with a conditional mean structure but compatible with the quantile regression. The existence of a strictly stationary solution is discussed, for which a necessary and sufficient condition is established. A doubly weighted quantile regression estimation procedure is introduced, where the first set of weights ensures the asymptotic normality of the estimator and the second set improves its efficiency through balancing individual quantile regression estimators across multiple quantile levels. Bayesian information criteria are proposed for model selection, and two goodness-of-fit tests are constructed to check the adequacy of the fitted conditional mean and conditional scale structures. Simulation studies indicate that the proposed inference tools perform well in finite samples, and an empirical example illustrates the usefulness of the new model.

Suggested Citation

  • Zhu, Qianqian & Zheng, Yao & Li, Guodong, 2018. "Linear double autoregression," Journal of Econometrics, Elsevier, vol. 207(1), pages 162-174.
    • Handle: RePEc:eee:econom:v:207:y:2018:i:1:p:162-174
    DOI: 10.1016/j.jeconom.2018.05.006
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    Cited by:

    1. Guo, Shaojun & Li, Dong & Li, Muyi, 2019. "Strict stationarity testing and GLAD estimation of double autoregressive models," Journal of Econometrics, Elsevier, vol. 211(2), pages 319-337.
    2. Kai Yang & Qingqing Zhang & Xinyang Yu & Xiaogang Dong, 2023. "Bayesian inference for a mixture double autoregressive model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 77(2), pages 188-207, May.
    3. Songhua Tan & Qianqian Zhu, 2022. "Asymmetric linear double autoregression," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(3), pages 371-388, May.
    4. Huan Gong & Dong Li, 2020. "On the three‐step non‐Gaussian quasi‐maximum likelihood estimation of heavy‐tailed double autoregressive models," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(6), pages 883-891, November.
    5. Mohit Garg & Suneel Sarswat, 2022. "The Design and Regulation of Exchanges: A Formal Approach," Papers 2210.05447, arXiv.org.
    6. Li, Dong & Tao, Yuxin & Yang, Yaxing & Zhang, Rongmao, 2023. "Maximum likelihood estimation for α-stable double autoregressive models," Journal of Econometrics, Elsevier, vol. 236(1).
    7. Guo, Shaojun & Li, Dong & Li, Muyi, 2018. "Strict Stationarity Testing and GLAD Estimation of Double Autoregressive Models," IRTG 1792 Discussion Papers 2018-049, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    8. Zhang, Wenjie & Quan, Hao & Srinivasan, Dipti, 2018. "Parallel and reliable probabilistic load forecasting via quantile regression forest and quantile determination," Energy, Elsevier, vol. 160(C), pages 810-819.

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    More about this item

    Keywords

    Conditional quantile estimation; Goodness-of-fit test; Heavy tail; Nonlinear time series model; Stationary solution;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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