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Copula-Based Nonlinear Quantile Autoregression

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Abstract

Parametric copulas are shown to be attractive devices for specifying quantile autoregressive models for nonlinear time-series. Estimation of local, quantile-specific copula-based time series models offers some salient advantages over classical global parametric approaches. Consistency and asymptotic normality of the proposed quantile estimators are established under mild conditions, allowing for global misspecification of parametric copulas and marginals, and without assuming any mixing rate condition. These results lead to a general framework for inference and model specification testing of extreme conditional value-at-risk for financial time series data.

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File URL: http://cowles.econ.yale.edu/P/cd/d16b/d1679.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1679.

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Length: 30 pages
Date of creation: Oct 2008
Date of revision:
Publication status: Published in Econometrics Journal (January 2009), 12(1): S50-S67
Handle: RePEc:cwl:cwldpp:1679

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Keywords: Quantile autoregression; Copula; Ergodic nonlinear Markov models;

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References

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  1. Beare, Brendan, 2008. "Copulas and Temporal Dependence," University of California at San Diego, Economics Working Paper Series qt2880q2jq, Department of Economics, UC San Diego.
  2. Koenker, Roger & Xiao, Zhijie, 2006. "Quantile Autoregression," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 980-990, September.
  3. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521608275.
  4. Weiss, Andrew A., 1991. "Estimating Nonlinear Dynamic Models Using Least Absolute Error Estimation," Econometric Theory, Cambridge University Press, vol. 7(01), pages 46-68, March.
  5. Chen, Xiaohong & Fan, Yanqin, 2006. "Estimation of copula-based semiparametric time series models," Journal of Econometrics, Elsevier, vol. 130(2), pages 307-335, February.
  6. Lars Peter Hansen & John Heaton & Erzo Luttmer, 1993. "Econometric Evaluation of Asset Pricing Models," NBER Technical Working Papers 0145, National Bureau of Economic Research, Inc.
  7. Robert F. Engle & Simone Manganelli, 2004. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 367-381, October.
  8. Andrew Patton, 2004. "Modelling Asymmetric Exchange Rate Dependence," Working Papers wp04-04, Warwick Business School, Financial Econometrics Research Centre.
  9. Pollard, David, 1985. "New Ways to Prove Central Limit Theorems," Econometric Theory, Cambridge University Press, vol. 1(03), pages 295-313, December.
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Cited by:
  1. Xiaohong Chen & Wei Biao Wu & Yanping Yi, 2009. "Efficient Estimation of Copula-based Semiparametric Markov Models," Cowles Foundation Discussion Papers 1691, Cowles Foundation for Research in Economics, Yale University, revised Mar 2009.
  2. Beare, Brendan K. & Seo, Juwon, 2012. "Time irreversible copula-based Markov Models," University of California at San Diego, Economics Working Paper Series qt31f8500p, Department of Economics, UC San Diego.
  3. Beare, Brendan K., 2010. "Archimedean Copulas and Temporal Dependence," University of California at San Diego, Economics Working Paper Series qt0xh8q1g3, Department of Economics, UC San Diego.

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