B. Cooper Boniece, José E. Figueroa-López, Yuchen Han
arXiv 2 Feb 2022 · Econometrics
arXiv:2202.00877 · PDF · DOI · OpenAlex · Extracted main text
Statistical inference for stochastic processes based on high-frequency observations has been an active research area for more than a decade. One of the most well-known and widely studied problems is that of estimation of the quadratic variation of the continuous component of an It\^o semimartingale with jumps. Several rate- and variance-efficient estimators have been proposed in the literature when the jump component is of bounded variation. However, to date, very few methods can deal with jumps of unbounded variation. By developing new high-order expansions of the truncated moments of a L\'evy process, we construct a new rate- and variance-efficient estimator for a class of L\'evy processes of unbounded variation, whose small jumps behave like those of a stable L\'evy process with Blumenthal-Getoor index less than $8/5$. The proposed method is based on a two-step debiasing procedure for the truncated realized quadratic variation of the process. Our Monte Carlo experiments indicate that the method outperforms other efficient alternatives in the literature in the setting covered by our theoretical framework.
appendix boundary found by appendix_command · 26% of the source is main text. Read the extracted text to check this.
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 | J. Jacod and V. Todorov (2014) Efficient Estimation of Integrated Volatility in Presence of Infinite Variation Jumps | 1.000 | 14 | 3 | 100% |
| 2 | J.E. Figueroa-López and S. Olafsson (2016) Short-Time Asymptotics for the Implied Volatility Skew under a Stochastic Volatility Model with Lévy Jumps | 0.811 | 4 | 2 | 100% |
| 3 | J.E. Figueroa-López, R. Gong, and C. Houdré (2016) High-order short-time expansions for ATM option prices of exponential Lévy models | 0.693 | 5 | 1 | 100% |
| 4 | F. Mies (2020) Rate-optimal estimation of the BlumenthalGetoor index of a Lévy process | 0.644 | 4 | 1 | 100% |
| 5 | P. Carr, H. Geman, D. Madan, and M. Yor (2002) The Fine Structure of Asset Returns: An Empirical Investigation | 0.644 | 2 | 2 | 100% |
| 6 | R. Cont and C. Mancini (2011) Nonparametric tests for pathwise properties of semimartingales | 0.585 | 3 | 1 | 100% |
| 7 | C. Amorino and A. Gloter (2020) Unbiased truncated quadratic variation for volatility estimation in jump diffusion processes | 0.511 | 2 | 1 | 100% |
| 8 | K. Sato (1999) Lévy Processes and Infinitely Divisible Distributions | 0.511 | 2 | 1 | 100% |
| 9 | C. Mancini (2009) Non-parametric threshold estimation for models with stochastic diffusion coefficient and jumps | 0.511 | 2 | 1 | 100% |
| 10 | J.E. Figueroa-López, R. Gong, and Y. Han (2021) Estimation of a Tempered Stable Lévy Model of Infinite Variation self | 0.464 | 10 | 3 | 10% |
Showing the top 10 of 21 scored citations.