Ruijun Bu, Degui Li, Oliver Linton, Hanchao Wang
arXiv 3 Jul 2023 · Econometrics · publishedEconometric Theory (2025) · 1 citations (OpenAlex)
arXiv:2307.01348 · PDF · DOI · OpenAlex · Extracted main text
In this paper, we consider estimating spot/instantaneous volatility matrices of high-frequency data collected for a large number of assets. We first combine classic nonparametric kernel-based smoothing with a generalised shrinkage technique in the matrix estimation for noise-free data under a uniform sparsity assumption, a natural extension of the approximate sparsity commonly used in the literature. The uniform consistency property is derived for the proposed spot volatility matrix estimator with convergence rates comparable to the optimal minimax one. For the high-frequency data contaminated by microstructure noise, we introduce a localised pre-averaging estimation method that reduces the effective magnitude of the noise. We then use the estimation tool developed in the noise-free scenario, and derive the uniform convergence rates for the developed spot volatility matrix estimator. We further combine the kernel smoothing with the shrinkage technique to estimate the time-varying volatility matrix of the high-dimensional noise vector. In addition, we consider large spot volatility matrix estimation in time-varying factor models with observable risk factors and derive the uniform convergence property. We provide numerical studies including simulation and empirical application to examine the performance of the proposed estimation methods in finite samples.
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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 | Fan, Furger \ Xiu (2016) Incorporating global industrial classification standard into portfolio allocation: A simple factor-based large covariance matrix… | 1.000 | 7 | 3 | 100% |
| 2 | Kanaya \ Kristensen (2016) Estimation of stochastic volatility models by nonparametric filtering | 1.000 | 5 | 3 | 100% |
| 3 | Dai, Lu \ Xiu (2019) Knowing factors or factor loadings, or neither? Evaluating estimators for large covariance matrices with noisy and asynchronous… | 0.965 | 10 | 6 | 90% |
| 4 | Aẗ-Sahalia, Kalnina \ Xiu (2020) High-frequency factor models and regressions | 0.928 | 4 | 3 | 100% |
| 5 | Tao, Wang \ Zhou (2013) Optimal sparse volatility matrix estimation for high-dimensional Itô processes with measurement errors | 0.928 | 4 | 3 | 100% |
| 6 | Chen \ Leng (2016) Dynamic covariance models | 0.874 | 5 | 2 | 100% |
| 7 | Wang \ Zou (2010) Vast volatility matrix estimation for high-frequency financial data | 0.843 | 4 | 3 | 75% |
| 8 | Bickel \ Levina (2008) Covariance regularization by thresholding | 0.843 | 3 | 3 | 100% |
| 9 | Barndorff-Nielsen \ Shephard (2004) Econometric analysis of realized covariation: High frequency based covariance, regression and correlation in financial economics | 0.843 | 3 | 3 | 100% |
| 10 | Kalnina \ Linton (2008) Estimating quadratic variation consistently in the presence of endogenous and diurnal measurement error | 0.843 | 3 | 3 | 100% |
Showing the top 10 of 59 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Spectral analysis of high-dimensional spot volatility matrix with applications | 0.644 | 2 | 2 |