Qi Wang, José E. Figueroa-López, Todd Kuffner
arXiv 11 Sep 2019 · Mathematics — Statistics Theory · publishedElectronic Journal of Statistics (2021)
arXiv:1909.04853 · PDF · DOI · OpenAlex · Extracted main text
Volatility estimation based on high-frequency data is key to accurately measure and control the risk of financial assets. A L\'{e}vy process with infinite jump activity and microstructure noise is considered one of the simplest, yet accurate enough, models for financial data at high-frequency. Utilizing this model, we propose a "purposely misspecified" posterior of the volatility obtained by ignoring the jump-component of the process. The misspecified posterior is further corrected by a simple estimate of the location shift and re-scaling of the log likelihood. Our main result establishes a Bernstein-von Mises (BvM) theorem, which states that the proposed adjusted posterior is asymptotically Gaussian, centered at a consistent estimator, and with variance equal to the inverse of the Fisher information. In the absence of microstructure noise, our approach can be extended to inferences of the integrated variance of a general It\^o semimartingale. Simulations are provided to demonstrate the accuracy of the resulting credible intervals, and the frequentist properties of the approximate Bayesian inference based on the adjusted posterior.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Martin, R., Ouyang, C. and Domagni, F (2018) ‘Purposely misspecified’ posterior inference on the volatility of a jump diffusion process | 1.000 | 11 | 4 | 100% |
| 2 | Mancini, C (2009) Non-parametric Threshold Estimation for Models with Stochastic Diffusion Coefficient and Jumps | 1.000 | 10 | 5 | 100% |
| 3 | Jing,B., Liu, Z. and Kong,X (2014) On the Estimation of Integrated Volatility With Jumps and Microstructure Noise | 1.000 | 7 | 4 | 100% |
| 4 | Cont, R. and Mancini, C (2011) Nonparametric tests for pathwise properties of semimartingales | 1.000 | 5 | 3 | 100% |
| 5 | Jacod, J., Li, Y, Mykland, P., Podolskij, M. and Vetter M (2009) Microstructure noise in the continuous case: The pre-averaging approach | 0.928 | 4 | 3 | 100% |
| 6 | Kleijn, B.J.K. and van der Vaart, A.W (2012) The Bernstein-von Mises theorem under misspecification | 0.874 | 5 | 2 | 100% |
| 7 | Jacod, J. and Protter, P.E (2012) Discretization of Processes | 0.737 | 4 | 3 | 50% |
| 8 | Gloter, A. and Jacod, J (2001) Diffusions with measurement errors. II. Optimal estimators | 0.737 | 4 | 3 | 50% |
| 9 | Li, H and Wells, M. and Yu, C (2008) A Bayesian Analysis of Return Dynamics with Lévy Jumps | 0.737 | 3 | 2 | 100% |
| 10 | Jacod J (2008) Asymptotic properties of realized power variations and related functionals of semimartingales | 0.644 | 3 | 2 | 67% |
Showing the top 10 of 39 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Estimation of Tempered Stable Lévy Models of Infinite Variation | 0.405 | 1 | 1 |