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Modeling autoregressive conditional skewness and kurtosis with multi-quantile CAViaR

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  • Manganelli, Simone
  • White, Halbert
  • Kim, Tae-Hwan

Abstract

Engle and Manganelli (2004) propose CAViaR, a class of models suitable for estimating conditional quantiles in dynamic settings. Engle and Manganelli apply their approach to the estimation of Value at Risk, but this is only one of many possible applications. Here we extend CAViaR models to permit joint modeling of multiple quantiles, Multi-Quantile (MQ) CAViaR. We apply our new methods to estimate measures of conditional skewness and kurtosis defined in terms of conditional quantiles, analogous to the unconditional quantile-based measures of skewness and kurtosis studied by Kim and White (2004). We investigate the performance of our methods by simulation, and we apply MQ-CAViaR to study conditional skewness and kurtosis of S&P 500 daily returns. JEL Classification: C13, C32

Suggested Citation

  • Manganelli, Simone & White, Halbert & Kim, Tae-Hwan, 2008. "Modeling autoregressive conditional skewness and kurtosis with multi-quantile CAViaR," Working Paper Series 957, European Central Bank.
  • Handle: RePEc:ecb:ecbwps:2008957
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    References listed on IDEAS

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    Cited by:

    1. Bouri, Elie & Shahzad, Syed Jawad Hussain & Raza, Naveed & Roubaud, David, 2018. "Oil volatility and sovereign risk of BRICS," Energy Economics, Elsevier, vol. 70(C), pages 258-269.
    2. Charle Augusto Llondoño, 2011. "Regresión del cuantil aplicada al modelo de redes neuronales artificiales. Una aproximación de la estructura CAVIAR para el mercado de valores colombiano," Revista ESPE - Ensayos Sobre Política Económica, Banco de la República - ESPE, vol. 29(64), pages 62-109, July.
    3. Ashoka Mody & Milan Nedeljkovic, 2018. "Central Bank Policies and Financial Markets: Lessons from the Euro Crisis," CESifo Working Paper Series 7400, CESifo Group Munich.
    4. Georgios Moratis & Plutarchos Sakellaris, 2017. "Measuring the systemic importance of banks," Working Papers 240, Bank of Greece.
    5. Katarzyna Kopczewska, 2014. "L-moments skewness and kurtosis as measures of regional convergence and cohesion," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 68(4), pages 251-266, November.
    6. White, Halbert & Kim, Tae-Hwan & Manganelli, Simone, 2015. "VAR for VaR: Measuring tail dependence using multivariate regression quantiles," Journal of Econometrics, Elsevier, vol. 187(1), pages 169-188.
    7. Krishnakumar, Jaya & Kabili, Andi & Roko, Ilir, 2012. "Estimation of SEM with GARCH errors," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3153-3181.
    8. Duran-Vazquez, Rocio & Lorenzo-Valdes, Arturo & Ruiz-Porras, Antonio, 2013. "Un modelo GARCH con asimetria condicional autorregresiva para modelar series de tiempo: Una aplicacion para los rendimientos del Indice de Precios y Cotizaciones de la BMV
      [A GARCH model with autor
      ," MPRA Paper 46328, University Library of Munich, Germany.
    9. Andrade, P. & Ghysels, E. & Idier, J., 2012. "Tails of Inflation Forecasts and Tales of Monetary Policy," Working papers 407, Banque de France.
    10. Hubner, Stefan, 2016. "Topics in nonparametric identification and estimation," Other publications TiSEM 08fce56b-3193-46e0-871b-0, Tilburg University, School of Economics and Management.
    11. Shih-Kang Chao & Wolfgang K. Härdle & Ming Yuan, 2015. "Factorisable Sparse Tail Event Curves," SFB 649 Discussion Papers SFB649DP2015-034, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    12. White, Halbert & Kim, Tae-Hwan & Manganelli, Simone, 2010. "VAR for VaR: measuring systemic risk using multivariate regression quantiles," MPRA Paper 35372, University Library of Munich, Germany.
    13. Tae-Hwan Kim & Christophe Muller, 2012. "Bias Transmission and Variance Reduction in Two-Stage Quantile Regression," Working Papers halshs-00793372, HAL.
    14. Ashoka Mody & Milan Nedeljkovic, 2018. "Central Bank Policies and Financial Markets: Lessons from the Euro Crisis," Working Papers 253, Princeton University, Department of Economics, Center for Economic Policy Studies..
    15. Shahzad, Syed Jawad Hussain & Rehman, Mobeen Ur & Jammazi, Rania, 2019. "Spillovers from oil to precious metals: Quantile approaches," Resources Policy, Elsevier, vol. 61(C), pages 508-521.
    16. Syed Jawad Hussain Shahzad & Naveed Raza & David Roubaud & Jose Arreola Hernandez & Stelios Bekiros, 2019. "Gold as Safe Haven for G-7 Stocks and Bonds: A Revisit," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 17(4), pages 885-912, December.
    17. Durán-Vázquez, Rocio & Lorenzo-Valdes, Arturo & Ruiz-Porras, Antonio, 2012. "Un modelo GARCH con asimetría condicional autorregresiva para modelar series de tiempo: Una aplicación para el Indice de Precios y Cotizaciones
      [A GARCH model with autorregresive conditional asymme
      ," MPRA Paper 42548, University Library of Munich, Germany.
    18. Huo, Lijuan & Kim, Tae-Hwan & Kim, Yunmi, 2012. "Robust estimation of covariance and its application to portfolio optimization," Finance Research Letters, Elsevier, vol. 9(3), pages 121-134.

    More about this item

    Keywords

    Asset returns; CAViaR; conditional quantiles; Dynamic quantiles; Kurtosis; Skewness.;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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