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Conditional Quantile Estimation for GARCH Models

Author

Listed:
  • Zhijie Xiao

    () (Boston College)

  • Roger Koenker

    (University of Illinois Urbana-Champaign)

Abstract

Conditional quantile estimation is an essential ingredient in modern risk management. Although GARCH processes have proven highly successful in modeling financial data it is generally recognized that it would be useful to consider a broader class of processes capable of representing more flexibly both asymmetry and tail behavior of conditional returns distributions. In this paper, we study estimation of conditional quantiles for GARCH models using quantile regression. Quantile regression estimation of GARCH models is highly nonlinear; we propose a simple and effective two-step approach of quantile regression estimation for linear GARCH time series. In the first step, we employ a quan- tile autoregression sieve approximation for the GARCH model by combining information over different quantiles; second stage estimation for the GARCH model is then carried out based on the first stage minimum distance estimation of the scale process of the time series. Asymptotic properties of the sieve approximation, the minimum distance estimators, and the final quantile regression estimators employing generated regressors are studied. These results are of independent interest and have applications in other quantile regression settings. Monte Carlo and empirical application results indicate that the proposed estimation methods outperform some existing conditional quantile estimation methods.

Suggested Citation

  • Zhijie Xiao & Roger Koenker, 2009. "Conditional Quantile Estimation for GARCH Models," Boston College Working Papers in Economics 725, Boston College Department of Economics.
  • Handle: RePEc:boc:bocoec:725
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    References listed on IDEAS

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    4. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
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    Cited by:

    1. Massimiliano Caporin & Loriana Pelizzon & Francesco Ravazzolo & Roberto Rigobon, 2012. "Measuring sovereign contagion in Europe," Working Paper 2012/05, Norges Bank.
    2. Cathy Chen & Richard Gerlach, 2013. "Semi-parametric quantile estimation for double threshold autoregressive models with heteroskedasticity," Computational Statistics, Springer, vol. 28(3), pages 1103-1131, June.
    3. Alessandra Pasqualina Viola & Marcelo Cabus Klotzle & Antonio Carlos Figueiredo Pinto & Wagner Piazza Gaglianone, 2017. "Predicting Exchange Rate Volatility in Brazil: an approach using quantile autoregression," Working Papers Series 466, Central Bank of Brazil, Research Department.

    More about this item

    Keywords

    Quantile Regression; GARCH; Value-at-Risk;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • 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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