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Assessing Tail Risk Using Expectile Regressions with Partially Varying Coefficients

Author

Listed:
  • Zongwu Cai

    (Department of Economics, The University of Kansa)

  • Ying Fang

    (The Wang Yanan Institute for Studies in Economics, Xiamen University, Xiamen, China)

  • Dingshi Tian

    (The Wang Yanan Institute for Studies in Economics, Xiamen University, Xiamen, China)

Abstract

To characterize heteroskedasticity and nonlinearity as well as asymmetry in tail risk, this paper investigates a class of conditional (dynamic) expectile models with partially varying coefficients in which some coefficients are allowed to be constants but others are allowed to be unknown functions of random variables. A three-stage estimation procedure is proposed to estimate both the parametric constant coefficients and nonparametric functional coefficients, and their asymptotic properties are investigated under time series context, together with a new simple and easily implemented test for testing the goodness of fit of models and a bandwidth selector based on newly defined cross-validatory estimation for the expected forecasting expectile errors. The proposed methodology is data-analytic and of sufficient flexibility to analyze complex and multivariate nonlinear structures without suffering from the curse of dimensionality. Finally, the proposed model is illustrated by simulated data and applied to analyzing the daily data of the S&P500 return series.

Suggested Citation

  • Zongwu Cai & Ying Fang & Dingshi Tian, 2018. "Assessing Tail Risk Using Expectile Regressions with Partially Varying Coefficients," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201804, University of Kansas, Department of Economics, revised Oct 2018.
    • Handle: RePEc:kan:wpaper:201804
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    File URL: http://www2.ku.edu/~kuwpaper/2018Papers/201804.pdf
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    References listed on IDEAS

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    1. Cai, Zongwu, 2002. "Two-Step Likelihood Estimation Procedure for Varying-Coefficient Models," Journal of Multivariate Analysis, Elsevier, vol. 82(1), pages 189-209, July.
    2. Kuan, Chung-Ming & Yeh, Jin-Huei & Hsu, Yu-Chin, 2009. "Assessing value at risk with CARE, the Conditional Autoregressive Expectile models," Journal of Econometrics, Elsevier, vol. 150(2), pages 261-270, June.
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    8. Cai, Zongwu & Fan, Jianqing & Yao, Qiwei, 2000. "Functional-coefficient regression models for nonlinear time series," LSE Research Online Documents on Economics 6314, London School of Economics and Political Science, LSE Library.
    9. Cai, Zongwu & Xiao, Zhijie, 2012. "Semiparametric quantile regression estimation in dynamic models with partially varying coefficients," Journal of Econometrics, Elsevier, vol. 167(2), pages 413-425.
    10. Jones, M. C., 1994. "Expectiles and M-quantiles are quantiles," Statistics & Probability Letters, Elsevier, vol. 20(2), pages 149-153, May.
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    Cited by:

    1. Dingshi Tian & Zongwu Cai & Ying Fang, 2018. "Econometric Modeling of Risk Measures: A Selective Review of the Recent Literature," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201807, University of Kansas, Department of Economics, revised Oct 2018.

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    More about this item

    Keywords

    Expectile; Heteroskedasticity; Nonlinearity; Varying Coefficients; Tail Risk;
    All these keywords.

    JEL classification:

    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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