Kim Christensen, Mark Podolskij, Nopporn Thamrongrat, Bezirgen Veliyev
arXiv 23 Jan 2026 · Econometrics
arXiv:2601.16668 · PDF · Extracted main text
In this paper, we show how to estimate the asymptotic (conditional) covariance matrix, which appears in central limit theorems in high-frequency estimation of asset return volatility. We provide a recipe for the estimation of this matrix by subsampling; an approach that computes rescaled copies of the original statistic based on local stretches of high-frequency data, and then it studies the sampling variation of these. We show that our estimator is consistent both in frictionless markets and models with additive microstructure noise. We derive a rate of convergence for it and are also able to determine an optimal rate for its tuning parameters (e.g., the number of subsamples). Subsampling does not require an extra set of estimators to do inference, which renders it trivial to implement. As a variance-covariance matrix estimator, it has the attractive feature that it is positive semi-definite by construction. Moreover, the subsampler is to some extent automatic, as it does not exploit explicit knowledge about the structure of the asymptotic covariance. It therefore tends to adapt to the problem at hand and be robust against misspecification of the noise process. As such, this paper facilitates assessment of the sampling errors inherent in high-frequency estimation of volatility. We highlight the finite sample properties of the subsampler in a Monte Carlo study, while some initial empirical work demonstrates its use to draw feasible inference about volatility in financial markets.
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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 | I. Kalnina (2011) Subsampling high frequency data | 1.000 | 7 | 3 | 100% |
| 2 | O. E. Barndorff-Nielsen and P. R. Hansen and A. Lunde and N. Shephard (2008) Designing realized kernels to measure the ex post variation of equity prices in the presence of noise | 0.928 | 4 | 3 | 100% |
| 3 | M. Podolskij and M. Vetter (2009) Bipower-type estimation in a noisy diffusion setting self | 0.918 | 22 | 5 | 77% |
| 4 | P. A. Mykland and L. Zhang (2017) Assessment of uncertainty in high frequency data: The observed asymptotic variance | 0.874 | 9 | 2 | 100% |
| 5 | J. Jacod and P. E. Protter (2012) Discretization of Processes | 0.843 | 4 | 3 | 75% |
| 6 | J. Jacod and Y. Li and P. A. Mykland and M. Podolskij and M. Vetter (2009) Microstructure noise in the continuous case: The pre-averaging approach self | 0.843 | 3 | 3 | 100% |
| 7 | L. Zhang and P. A. Mykland and Y. Aït-Sahalia (2005) A tale of two time scales: determining integrated volatility with noisy high-frequency data | 0.843 | 3 | 3 | 100% |
| 8 | P. R. Hansen and A. Lunde (2006) Realized variance and market microstructure noise | 0.811 | 4 | 2 | 100% |
| 9 | N. Hautsch and M. Podolskij (2013) Pre-averaging based estimation of quadratic variation in the presence of noise and jumps: Theory, implementation, and empirical… self | 0.811 | 4 | 2 | 100% |
| 10 | Y. Aït-Sahalia and P. A. Mykland and L. Zhang (2011) Ultra high frequency volatility estimation with dependent microstructure noise | 0.737 | 3 | 2 | 100% |
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