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LADE-based inferences for autoregressive models with heavy-tailed G-GARCH(1, 1) noise

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  • Zhang, Xingfa
  • Zhang, Rongmao
  • Li, Yuan
  • Ling, Shiqing

Abstract

This paper explores the least absolute deviation (LAD) estimator of the autoregressive model with heavy-tailed G-GARCH(1, 1) noise. When the tail index α∈(1,2], it is shown that the LAD estimator asymptotically converges to a linear function of a series of α-stable random vectors with a rate of convergence n1−1/α. The result is significantly different from that of the corresponding least square estimator which is not consistent, and partially solves the problem on the asymptoticity of the LAD estimator when the tail index is less than 2. A simulation study is carried out to assess the performance of the LAD estimator and a real example is given to illustrate this approach.

Suggested Citation

  • Zhang, Xingfa & Zhang, Rongmao & Li, Yuan & Ling, Shiqing, 2022. "LADE-based inferences for autoregressive models with heavy-tailed G-GARCH(1, 1) noise," Journal of Econometrics, Elsevier, vol. 227(1), pages 228-240.
    • Handle: RePEc:eee:econom:v:227:y:2022:i:1:p:228-240
    DOI: 10.1016/j.jeconom.2020.06.011
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    More about this item

    Keywords

    G-GARCH-model; AR model; Heavy tails; LADE;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: 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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