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Exact Bayesian moment based inference for the distribution of the small-time movements of an Itô semimartingale

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  • Ronald Gallant, A.
  • Tauchen, George

Abstract

We modify the Gallant and Tauchen (1996) efficient method of moments (EMM) method to perform exact Bayesian inference, where exact means no reliance on asymptotic approximations. We use this modification to evaluate the empirical plausibility of recent predictions from high frequency financial theory regarding the small-time movements of an Itô semimartingale. The theory indicates that the probability distribution of the small moves should be locally stable around the origin. It makes no predictions regarding large rare jumps, which get filtered out. Our exact Bayesian procedure imposes support conditions on parameters as implied by this theory. The empirical application uses S&P Index options extending over a wide range of moneyness, including deep out of the money puts. The evidence is consistent with a locally stable distribution valid over most of the support of the observed data while mildly failing in the extreme tails, about which the theory makes no prediction. We undertake diagnostic checks on all aspects of the procedure. In particular, we evaluate the distributional assumptions regarding a semi-pivotal statistic, and we test by Monte Carlo that the posterior distribution is properly centered with short credibility intervals. Taken together, our results suggest a more important role than previously thought for pure jump-like models with diminished, if not absent, diffusive component.

Suggested Citation

  • Ronald Gallant, A. & Tauchen, George, 2018. "Exact Bayesian moment based inference for the distribution of the small-time movements of an Itô semimartingale," Journal of Econometrics, Elsevier, vol. 205(1), pages 140-155.
  • Handle: RePEc:eee:econom:v:205:y:2018:i:1:p:140-155
    DOI: 10.1016/j.jeconom.2018.03.008
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    References listed on IDEAS

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    1. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
    2. Ole E. Barndorff-Nielsen & Neil Shephard, 2006. "Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation," Journal of Financial Econometrics, Oxford University Press, vol. 4(1), pages 1-30.
    3. Chernozhukov, Victor & Hong, Han, 2003. "An MCMC approach to classical estimation," Journal of Econometrics, Elsevier, vol. 115(2), pages 293-346, August.
    4. Gallant, A. Ronald & Tauchen, George, 1996. "Which Moments to Match?," Econometric Theory, Cambridge University Press, vol. 12(4), pages 657-681, October.
    5. Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-390, March.
    6. Per A. Mykland & Lan Zhang, 2009. "Inference for Continuous Semimartingales Observed at High Frequency," Econometrica, Econometric Society, vol. 77(5), pages 1403-1445, September.
    7. Andersen, Torben G. & Bondarenko, Oleg & Todorov, Viktor & Tauchen, George, 2015. "The fine structure of equity-index option dynamics," Journal of Econometrics, Elsevier, vol. 187(2), pages 532-546.
    8. Garcia, René & Renault, Eric & Veredas, David, 2011. "Estimation of stable distributions by indirect inference," Journal of Econometrics, Elsevier, vol. 161(2), pages 325-337, April.
    9. A. Ronald Gallant, 2016. "Reflections on the Probability Space Induced by Moment Conditions with Implications for Bayesian Inference," Journal of Financial Econometrics, Oxford University Press, vol. 14(2), pages 229-247.
    10. Yacine Aït-Sahalia & Jean Jacod, 2014. "High-Frequency Financial Econometrics," Economics Books, Princeton University Press, edition 1, number 10261.
    11. Ole E. Barndorff-Nielsen, 2004. "Power and Bipower Variation with Stochastic Volatility and Jumps," Journal of Financial Econometrics, Oxford University Press, vol. 2(1), pages 1-37.
    12. Fenton, Victor M. & Gallant, A. Ronald, 1996. "Qualitative and asymptotic performance of SNP density estimators," Journal of Econometrics, Elsevier, vol. 74(1), pages 77-118, September.
    13. Coppejans, Mark & Gallant, A. Ronald, 2002. "Cross-validated SNP density estimates," Journal of Econometrics, Elsevier, vol. 110(1), pages 27-65, September.
    14. A. Ronald Gallant, 2016. "Reflections on the Probability Space Induced by Moment Conditions with Implications for Bayesian Inference — Author Response to Comments," Journal of Financial Econometrics, Oxford University Press, vol. 14(2), pages 284-294.
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    More about this item

    Keywords

    High-frequency data; Activity index; Efficient method of moments; Semimartingale; Specification test; Spot variance; Stochastic volatility;
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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