Asymptotic Normality and Finite-Sample Robustness of the Fourier Spot Volatility Estimator in the Presence of Microstructure Noise
Bibliographic Data
| ID | 19418366 |
|---|---|
| Authors | Maria Elvira Mancino (0000-0001-9146-4107, University of Florence), Tommaso Mariotti (0009-0007-4431-9442, University of Turin, corresponding author), Giacomo Toscano (0000-0002-1987-6470, University of Florence) |
| Year | 2025 |
| Volume | 43 |
| Issue | 4 |
| Pages | 850-861 |
| Publication date | 2025-10-02 |
| Open Access | No |
| Type | ARTICLE |
| Venue | Journal of Business and Economic Statistics (JOURNAL) |
| Journal identifiers | ISSN: 0735-0015 • E-ISSN: 1537-2707 |
| Publisher | Informa UK Limited (PUBLISHER • GB) |
| DOI | 10.1080/07350015.2024.2435910 |
| OpenAlex | W4404965443 |
| Language | EN |
| References cited | 40 |
We study the efficiency and robustness of the Fourier spot volatility estimator when high-frequency prices are contaminated by microstructure noise. First, we show that the estimator is consistent and asymptotically efficient in the presence of additive noise, establishing a Central Limit Theorem (CLT) with the optimal rate of convergence n1/8. Additionally, we complete the asymptotic theory in the absence of noise, obtaining a CLT with the optimal rate of convergence n1/4. Feasible CLTs with the optimal convergence rate are also obtained, by proving the consistency of the Fourier estimators of the spot volatility of volatility and the quarticity in the presence of noise. Second, we introduce a feasible method for selecting the cutting frequencies of the estimator in the presence of noise, based on the optimization of the integrated asymptotic variance. Finally, we provide support to the accuracy and robustness of the method by means of a numerical study and an empirical exercise, which is conducted using tick-by-tick prices of three U.S. stocks with different liquidity
Asymptotic distribution · Composite material · Econometrics · Estimator · Fourier transform · Mathematical analysis · Microstructure · Normality · Statistics · Chemistry · Financial Risk and Volatility Modeling · Materials Science · Mathematics · Statistical Methods and Inference · Stochastic processes and financial applications · Applied Mathematics
| Highly cited | No |
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