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Estimation of Time Varying Skewness and Kurtosis with an Application to Value at Risk

Listed author(s):
  • Dark Jonathan Graeme

    ()

    (University of Melbourne)

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    This paper generalizes the Hyperbolic Asymmetric Power ARCH (HYAPARCH) model to allow for time varying skewness and kurtosis in the conditional distribution. This is done by modeling the conditional skewness and degrees of freedom of the skewed Student's t distribution of Lambert and Laurent (2001) as a function of the conditioning information. The proposed specification nests a large number of models in the literature and represents the first attempt to jointly model long memory in volatility and time variation in the third and fourth moments. The finite sample properties of MLE for this class of model are examined. The results indicate that the ARCH class of processes with time varying skewness can be reliably estimated with realistic sample sizes. Simulations and empirical evidence are unable to replicate the findings of Harvey and Siddique (1999), that accounting for time varying skewness reduces the persistence and asymmetry properties of the conditional variance. Simulations also suggest that time varying kurtosis estimation must be viewed with caution, because it can be difficult to identify in the presence of ARCH effects. Application of the HYAPARCH model with time varying skewness and degrees of freedom illustrates the usefulness of the proposed approach. Out of sample forecasts of the value at risk (VaR) however, generally support parsimonious models that assume conditional normality. When forecasting VaR, skewness and leptokurtosis in the unconditional return distribution is generally better captured via an asymmetric conditional variance model with Gaussian innovations.

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    Article provided by De Gruyter in its journal Studies in Nonlinear Dynamics & Econometrics.

    Volume (Year): 14 (2010)
    Issue (Month): 2 (March)
    Pages: 1-50

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    Handle: RePEc:bpj:sndecm:v:14:y:2010:i:2:n:3
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    1. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, 09.
    2. Lo, Andrew W, 1991. "Long-Term Memory in Stock Market Prices," Econometrica, Econometric Society, vol. 59(5), pages 1279-1313, September.
    3. GIOT, Pierre & LAURENT, Sébastien, 2001. "Value-at-risk for long and short trading positions," CORE Discussion Papers 2001022, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Gallant, A. Ronald & Hsu, Chien-Te & Tauchen, George, 2000. "Using Daily Range Data to Calibrate Volatility Diffusions and Extract the Forward Integrated Variance," Working Papers 00-04, Duke University, Department of Economics.
    5. Francis X. Diebold & Atsushi Inoue, 2000. "Long Memory and Regime Switching," NBER Technical Working Papers 0264, National Bureau of Economic Research, Inc.
    6. Lobato, Ignacio N & Savin, N E, 1998. "Real and Spurious Long-Memory Properties of Stock-Market Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 261-268, July.
    7. Giovanni Barone Adesi & Patrick Gagliardini & Giovanni Urga, 2004. "Testing Asset Pricing Models With Coskewness," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 474-485, October.
    8. Lee, Hyung S. & Amsler, Christine, 1997. "Consistency of the KPSS unit root test against fractionally integrated alternative," Economics Letters, Elsevier, vol. 55(2), pages 151-160, August.
    9. Markku Lanne & Pentti Saikkonen, 2005. "Modeling Conditional Skewness in Stock Returns," Economics Working Papers ECO2005/14, European University Institute.
    10. Campbell R. Harvey & Akhtar Siddique, 2000. "Conditional Skewness in Asset Pricing Tests," Journal of Finance, American Finance Association, vol. 55(3), pages 1263-1295, 06.
    11. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).
    12. Jondeau, Eric & Rockinger, Michael, 2003. "Conditional volatility, skewness, and kurtosis: existence, persistence, and comovements," Journal of Economic Dynamics and Control, Elsevier, vol. 27(10), pages 1699-1737, August.
    13. Anders Wilhelmsson, 2009. "Value at Risk with time varying variance, skewness and kurtosis--the NIG-ACD model," Econometrics Journal, Royal Economic Society, vol. 12(1), pages 82-104, 03.
    14. Harvey, Campbell R. & Siddique, Akhtar, 1999. "Autoregressive Conditional Skewness," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(04), pages 465-487, December.
    15. Whitney K. Newey & Douglas G. Steigerwald, 1997. "Asymptotic Bias for Quasi-Maximum-Likelihood Estimators in Conditional Heteroskedasticity Models," Econometrica, Econometric Society, vol. 65(3), pages 587-600, May.
    16. John Elder & Hyun J. Jin, 2007. "Long memory in commodity futures volatility: A wavelet perspective," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 27(5), pages 411-437, 05.
    17. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    18. repec:hal:journl:halshs-00179275 is not listed on IDEAS
    19. Rockinger, M. & Jondeau, E., 2001. "Entropy Densities: with an Application to Autoregressive Conditional Skewness and Kurtosis," Working papers 79, Banque de France.
    20. Nour Meddahi & Éric Renault, 2000. "Temporal Aggregation of Volatility Models," CIRANO Working Papers 2000s-22, CIRANO.
    21. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. " On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    22. Granger, Clive W. J. & Hyung, Namwon, 2004. "Occasional structural breaks and long memory with an application to the S&P 500 absolute stock returns," Journal of Empirical Finance, Elsevier, vol. 11(3), pages 399-421, June.
    23. Abdou Kâ Diongue & Dominique Guegan, 2007. "The Stationary Seasonal Hyperbolic Asymmetric Power ARCH model," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00179275, HAL.
    24. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    25. Ding, Zhuanxin & Granger, Clive W. J., 1996. "Modeling volatility persistence of speculative returns: A new approach," Journal of Econometrics, Elsevier, vol. 73(1), pages 185-215, July.
    26. Lux, Thomas, 2003. "The multi-fractal model of asset returns: Its estimation via GMM and its use for volatility forecasting," Economics Working Papers 2003-13, Christian-Albrechts-University of Kiel, Department of Economics.
    27. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2001. "Modeling and Forecasting Realized Volatility," Center for Financial Institutions Working Papers 01-01, Wharton School Center for Financial Institutions, University of Pennsylvania.
    28. Heston, Steven L & Nandi, Saikat, 2000. "A Closed-Form GARCH Option Valuation Model," Review of Financial Studies, Society for Financial Studies, vol. 13(3), pages 585-625.
    29. Anil K. Bera & Sangkyu Lee, 1993. "Information Matrix Test, Parameter Heterogeneity and ARCH: A Synthesis," Review of Economic Studies, Oxford University Press, vol. 60(1), pages 229-240.
    30. Leon, Angel & Rubio, Gonzalo & Serna, Gregorio, 2005. "Autoregresive conditional volatility, skewness and kurtosis," The Quarterly Review of Economics and Finance, Elsevier, vol. 45(4-5), pages 599-618, September.
    31. Andersen, Torben G & Bollerslev, Tim, 1997. " Heterogeneous Information Arrivals and Return Volatility Dynamics: Uncovering the Long-Run in High Frequency Returns," Journal of Finance, American Finance Association, vol. 52(3), pages 975-1005, July.
    32. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    33. Davidson, James, 2004. "Moment and Memory Properties of Linear Conditional Heteroscedasticity Models, and a New Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 22(1), pages 16-29, January.
    34. Andersen, Torben G. & Bollerslev, Tim, 1997. "Intraday periodicity and volatility persistence in financial markets," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 115-158, June.
    35. Fang, Hsing & Lai, Tsong-Yue, 1997. "Co-Kurtosis and Capital Asset Pricing," The Financial Review, Eastern Finance Association, vol. 32(2), pages 293-307, May.
    36. Brännäs, Kurt & Nordman, Niklas, 2001. "Conditional Skewness Modelling for Stock Returns," Umeå Economic Studies 562, Umeå University, Department of Economics.
    37. Y. K. Tse, 1998. "The conditional heteroscedasticity of the yen-dollar exchange rate," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(1), pages 49-55.
    38. Torben G. Andersen & Tim Bollerslev, 1998. "Deutsche Mark-Dollar Volatility: Intraday Activity Patterns, Macroeconomic Announcements, and Longer Run Dependencies," Journal of Finance, American Finance Association, vol. 53(1), pages 219-265, 02.
    39. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    40. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
    41. Charlie Charoenwong & Nattawut Jenwittayaroje & Buen Sin Low, 2009. "Who knows more about future currency volatility?," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 29(3), pages 270-295, 03.
    42. Ederington, Louis H, 1979. "The Hedging Performance of the New Futures Markets," Journal of Finance, American Finance Association, vol. 34(1), pages 157-170, March.
    43. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-547, August.
    44. Bollerslev, Tim & Ole Mikkelsen, Hans, 1996. "Modeling and pricing long memory in stock market volatility," Journal of Econometrics, Elsevier, vol. 73(1), pages 151-184, July.
    45. Lobato, Ignacio N & Savin, N E, 1998. "Real and Spurious Long-Memory Properties of Stock-Market Data: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 280-283, July.
    46. Morten B. Jensen & Asger Lunde, 2001. "The NIG-S&ARCH model: a fat-tailed, stochastic, and autoregressive conditional heteroskedastic volatility model," Econometrics Journal, Royal Economic Society, vol. 4(2), pages 1-10.
    47. Guermat, Cherif & Harris, Richard D. F., 2002. "Forecasting value at risk allowing for time variation in the variance and kurtosis of portfolio returns," International Journal of Forecasting, Elsevier, vol. 18(3), pages 409-419.
    48. Liu, Ming, 2000. "Modeling long memory in stock market volatility," Journal of Econometrics, Elsevier, vol. 99(1), pages 139-171, November.
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