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Probabilistic and statistical properties of moment variations and their use in inference and estimation based on high frequency return data

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  • Lee Kyungsub

    (UNIST – School of Business Administration, Ulsan, Republic of Korea)

Abstract

We discuss the probabilistic properties of the variation based third and fourth moments of financial returns as estimators of the actual moments of the return distributions. The moment variations are defined under non-parametric assumptions with quadratic variation method but for the computational tractability, we use a square root stochastic volatility model for the derivations of moment conditions for estimations. Using the S&P 500 index high frequency data, the realized versions of the moment variations is used for the estimation of a stochastic volatility model. We propose a simple estimation method of a stochastic volatility model using the sample averages of the variations and ARMA estimation. In addition, we compare the results with a generalized method of moments estimation based on the successive relation between realized moments and their lagged values.

Suggested Citation

  • Lee Kyungsub, 2016. "Probabilistic and statistical properties of moment variations and their use in inference and estimation based on high frequency return data," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 20(1), pages 19-36, February.
    • Handle: RePEc:bpj:sndecm:v:20:y:2016:i:1:p:19-36:n:3
    DOI: 10.1515/snde-2014-0037
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    References listed on IDEAS

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    1. Nour Meddahi, 2003. "ARMA representation of integrated and realized variances," Econometrics Journal, Royal Economic Society, vol. 6(2), pages 335-356, December.
    2. Ole E. Barndorff‐Nielsen & Neil Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280, May.
    3. Jacinto Marabel Romo, 2014. "Pricing Forward Skew Dependent Derivatives. Multifactor Versus Single‐Factor Stochastic Volatility Models," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 34(2), pages 124-144, February.
    4. Bollerslev, Tim & Gibson, Michael & Zhou, Hao, 2011. "Dynamic estimation of volatility risk premia and investor risk aversion from option-implied and realized volatilities," Journal of Econometrics, Elsevier, vol. 160(1), pages 235-245, January.
    5. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    6. Harvey, Campbell R. & Siddique, Akhtar, 1999. "Autoregressive Conditional Skewness," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(4), pages 465-487, December.
    7. Garcia, René & Lewis, Marc-André & Pastorello, Sergio & Renault, Éric, 2011. "Estimation of objective and risk-neutral distributions based on moments of integrated volatility," Journal of Econometrics, Elsevier, vol. 160(1), pages 22-32, January.
    8. Per A. Mykland & Lan Zhang, 2009. "Inference for Continuous Semimartingales Observed at High Frequency," Econometrica, Econometric Society, vol. 77(5), pages 1403-1445, September.
    9. Bollerslev, Tim & Zhou, Hao, 2002. "Estimating stochastic volatility diffusion using conditional moments of integrated volatility," Journal of Econometrics, Elsevier, vol. 109(1), pages 33-65, July.
    10. Roman Kozhan & Anthony Neuberger & Paul Schneider, 2013. "The Skew Risk Premium in the Equity Index Market," The Review of Financial Studies, Society for Financial Studies, vol. 26(9), pages 2174-2203.
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