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

Publication ,  Journal Article
Ronald Gallant, A; Tauchen, G
Published in: Journal of Econometrics
July 1, 2018

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.

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Published In

Journal of Econometrics

DOI

EISSN

1872-6895

ISSN

0304-4076

Publication Date

July 1, 2018

Volume

205

Issue

1

Start / End Page

140 / 155

Related Subject Headings

  • Econometrics
  • 1403 Econometrics
  • 1402 Applied Economics
  • 0104 Statistics
 

Citation

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Ronald Gallant, A., & Tauchen, G. (2018). Exact Bayesian moment based inference for the distribution of the small-time movements of an Itô semimartingale. Journal of Econometrics, 205(1), 140–155. https://doi.org/10.1016/j.jeconom.2018.03.008
Ronald Gallant, A., and G. Tauchen. “Exact Bayesian moment based inference for the distribution of the small-time movements of an Itô semimartingale.” Journal of Econometrics 205, no. 1 (July 1, 2018): 140–55. https://doi.org/10.1016/j.jeconom.2018.03.008.
Ronald Gallant A, Tauchen G. Exact Bayesian moment based inference for the distribution of the small-time movements of an Itô semimartingale. Journal of Econometrics. 2018 Jul 1;205(1):140–55.
Ronald Gallant, A., and G. Tauchen. “Exact Bayesian moment based inference for the distribution of the small-time movements of an Itô semimartingale.” Journal of Econometrics, vol. 205, no. 1, July 2018, pp. 140–55. Scopus, doi:10.1016/j.jeconom.2018.03.008.
Ronald Gallant A, Tauchen G. Exact Bayesian moment based inference for the distribution of the small-time movements of an Itô semimartingale. Journal of Econometrics. 2018 Jul 1;205(1):140–155.
Journal cover image

Published In

Journal of Econometrics

DOI

EISSN

1872-6895

ISSN

0304-4076

Publication Date

July 1, 2018

Volume

205

Issue

1

Start / End Page

140 / 155

Related Subject Headings

  • Econometrics
  • 1403 Econometrics
  • 1402 Applied Economics
  • 0104 Statistics