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Modeling Tail Index With Autoregressive Conditional Pareto Model

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  • Zhouyu Shen
  • Yu Chen
  • Ruxin Shi

Abstract

We propose an autoregressive conditional Pareto (AcP) model based on the dynamic peaks over threshold method to model a dynamic tail index in the financial markets. Unlike the score-based approach which is widely used in many articles, we use an exponential function to model the tail index process for its intuitiveness and interpretability. Probabilistic properties of the AcP model and the statistical properties of its parameter estimators of maximum likelihood are studied in this article. Real data are used to show the advantages of AcP, especially, compared to the estimation volatility of GARCH model, the result of AcP is more sensitive to turmoil. The estimated tail index of AcP can accurately reflect the risk of the stock and may even play an early warning role to the turmoil of stock market. We also calculate the tail connectedness based on the estimated tail index of AcP and show that tail connectedness increases during period of turmoil, which is consistent with the result of the score-based approach.

Suggested Citation

  • Zhouyu Shen & Yu Chen & Ruxin Shi, 2022. "Modeling Tail Index With Autoregressive Conditional Pareto Model," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(1), pages 458-466, January.
    • Handle: RePEc:taf:jnlbes:v:40:y:2022:i:1:p:458-466
    DOI: 10.1080/07350015.2020.1832504
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    Cited by:

    1. Ke, Rui & Yang, Luyao & Tan, Changchun, 2022. "Forecasting tail risk for Bitcoin: A dynamic peak over threshold approach," Finance Research Letters, Elsevier, vol. 49(C).
    2. Yun Feng & Weijie Hou & Yuping Song, 2024. "Tail risk forecasting and its application to margin requirements in the commodity futures market," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 43(5), pages 1513-1529, August.
    3. Candia, Claudio & Herrera, Rodrigo, 2024. "An empirical review of dynamic extreme value models for forecasting value at risk, expected shortfall and expectile," Journal of Empirical Finance, Elsevier, vol. 77(C).
    4. Feng, Yun & Hou, Weijie & Song, Yuping, 2023. "Tail risk in the Chinese stock market: An AEV model on the maximal drawdowns," Finance Research Letters, Elsevier, vol. 58(PA).
    5. 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.

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