Nonparametric Test for Rough Volatility

• 成果类型: Article; Early Access
• 署名作者: Chong, Carsten H.; Todorov, Viktor
• 署名单位: Hong Kong University of Science & Technology; Northwestern University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2025.2495316
• 发表日期: 2025
• 关键词: INTEGRATED VOLATILITY; long memory; inference; price

摘要

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 uses 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 high-frequency financial data, we find evidence for rough volatility. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.