Kim Christensen, Ulrich Hounyo, Mark Podolskij
arXiv 23 Jan 2026 · Econometrics
arXiv:2601.16613 · PDF · Extracted main text
In this paper, we propose a nonparametric way to test the hypothesis that time-variation in intraday volatility is caused solely by a deterministic and recurrent diurnal pattern. We assume that noisy high-frequency data from a discretely sampled jump-diffusion process are available. The test is then based on asset returns, which are deflated by the seasonal component and therefore homoskedastic under the null. To construct our test statistic, we extend the concept of pre-averaged bipower variation to a general Itô semimartingale setting via a truncation device. We prove a central limit theorem for this statistic and construct a positive semi-definite estimator of the asymptotic covariance matrix. The $t$-statistic (after pre-averaging and jump-truncation) diverges in the presence of stochastic volatility and has a standard normal distribution otherwise. We show that replacing the true diurnal factor with a model-free jump- and noise-robust estimator does not affect the asymptotic theory. A Monte Carlo simulation also shows this substitution has no discernable impact in finite samples. The test is, however, distorted by small infinite-activity price jumps. To improve inference, we propose a new bootstrap approach, which leads to almost correctly sized tests of the null hypothesis. We apply the developed framework to a large cross-section of equity high-frequency data and find that the diurnal pattern accounts for a rather significant fraction of intraday variation in volatility, but important sources of heteroskedasticity remain present in the data.
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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 | Hounyo, Goncalves, and Meddahi (2017) Bootstrapping pre-averaged realized volatility under market microstructure noise | 1.000 | 10 | 3 | 100% |
| 2 | Podolskij and Vetter (2009) Bipower-type estimation in a noisy diffusion setting | 1.000 | 8 | 3 | 100% |
| 3 | Christensen, Oomen, and Podolskij (2014) Fact or friction: Jumps at ultra high frequency self | 1.000 | 5 | 4 | 100% |
| 4 | Jacod, Li, Mykland, Podolskij, and Vetter (2009) Microstructure noise in the continuous case: The pre-averaging approach | 1.000 | 5 | 4 | 100% |
| 5 | Barndorff-Nielsen, Hansen, Lunde, and Shephard (2008) Designing realized kernels to measure the ex post variation of equity prices in the presence of noise | 1.000 | 5 | 3 | 100% |
| 6 | Hounyo (2017) Bootstrapping integrated covariance matrix estimators in noisy jump-diffusion models with non-synchronous trading self | 0.928 | 4 | 3 | 100% |
| 7 | Andersen and Bollerslev (1997) Intraday periodicity and volatility persistence in financial markets | 0.811 | 4 | 2 | 100% |
| 8 | Boudt, Croux, and Laurent (2011) Robust estimation of intraweek periodicity in volatility and jump detection | 0.811 | 4 | 2 | 100% |
| 9 | Andersen and Bollerslev (1998) Deutsche Mark-Dollar volatility: Intraday activity patterns, macroeconomic announcements, and longer run dependencies | 0.737 | 3 | 2 | 100% |
| 10 | Andersen, Dobrev, and Schaumburg (2012) Jump-robust volatility estimation using nearest neighbour truncation | 0.737 | 3 | 2 | 100% |
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