Carsten H. Chong, Viktor Todorov
arXiv 15 Jul 2024 · Mathematics — Statistics Theory · publishedJournal of the American Statistical Association (2025) · 4 citations (OpenAlex)
arXiv:2407.10659 · PDF · DOI · OpenAlex · Extracted main text
We develop a nonparametric test for deciding whether volatility of an asset follows a standard semimartingale process, with paths of finite quadratic variation, or a rough process with paths of infinite quadratic variation. The test utilizes the fact that volatility is rough if and only if volatility increments are negatively autocorrelated at high frequencies. It is based on the sample autocovariance of increments of spot volatility estimates computed from high-frequency asset return data. By showing a feasible CLT for this statistic under the null hypothesis of semimartingale volatility paths, we construct a test with fixed asymptotic size and an asymptotic power equal to one. The test is derived under very general conditions for the data-generating process. In particular, it is robust to jumps with arbitrary activity and to the presence of market microstructure noise. In an application of the test to SPY high-frequency data, we find evidence for rough volatility.
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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 | J. Jacod and P. Protter (2012) Discretization of Processes, volume 67 of Stochastic Modelling and Applied Probability | 1.000 | 7 | 5 | 100% |
| 2 | J. Gatheral, T. Jaisson, and M. Rosenbaum (2018) Volatility is rough | 0.843 | 3 | 3 | 100% |
| 3 | M. Bennedsen, A. Lunde, and M. S. Pakkanen (2022) Decoupling the short- and long-term behavior of stochastic volatility | 0.811 | 4 | 2 | 100% |
| 4 | J. Jacod and A. N. Shiryaev (2003) Limit Theorems for Stochastic Processes, volume 288 of Grundlehren der mathematischen Wissenschaften [Fundamental Principles of… | 0.644 | 2 | 2 | 100% |
| 5 | X. Wang, W. Xiao, and J. Yu (2023) Modeling and forecasting realized volatility with the fractional Ornstein–Uhlenbeck process | 0.644 | 2 | 2 | 100% |
| 6 | O. E. Barndorff-Nielsen, J. M. Corcuera, and M. Podolskij (2011) Multipower variation for Brownian semistationary processes | 0.644 | 2 | 2 | 100% |
| 7 | R. Cont and P. Das (2024) Rough volatility: Fact or artefact? | 0.644 | 2 | 2 | 100% |
| 8 | C. H. Chong and V. Todorov (2024) A nonparametric test for rough volatility self | 0.644 | 2 | 2 | 100% |
| 9 | X. Liu, S. Shi, and J. Yu (2020) Persistent and rough volatility | 0.511 | 2 | 1 | 100% |
| 10 | Y. S. Mishura (2008) Stochastic Calculus for Fractional Brownian Motion and Related Processes, volume 1929 of Lecture Notes in Mathematics | 0.511 | 2 | 1 | 100% |
Showing the top 10 of 45 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Optimal Estimation for General Gaussian Processes | 0.405 | 1 | 1 |
| 2 | Spectral analysis of high-dimensional spot volatility matrix with applications | 0.405 | 1 | 1 |