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Symmetric positive semi-definite Fourier estimator of instantaneous variance-covariance matrix

Author

Listed:
  • Jir^o Akahori
  • Nien-Lin Liu
  • Maria Elvira Mancino
  • Tommaso Mariotti
  • Yukie Yasuda

Abstract

In this paper we propose an estimator of spot covariance matrix which ensure symmetric positive semi-definite estimations. The proposed estimator relies on a suitable modification of the Fourier covariance estimator in Malliavin and Mancino (2009) and it is consistent for suitable choices of the weighting kernel. The accuracy and the ability of the estimator to produce positive semi-definite covariance matrices is evaluated with an extensive numerical study, in comparison with the competitors present in the literature. The results of the simulation study are confirmed under many scenarios, that consider the dimensionality of the problem, the asynchronicity of data and the presence of several specification of market microstructure noise.

Suggested Citation

  • Jir^o Akahori & Nien-Lin Liu & Maria Elvira Mancino & Tommaso Mariotti & Yukie Yasuda, 2023. "Symmetric positive semi-definite Fourier estimator of instantaneous variance-covariance matrix," Papers 2304.04372, arXiv.org.
    • Handle: RePEc:arx:papers:2304.04372
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    References listed on IDEAS

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    1. Markus Bibinger & Nikolaus Hautsch & Peter Malec & Markus Reiss, 2019. "Estimating the Spot Covariation of Asset Prices—Statistical Theory and Empirical Evidence," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(3), pages 419-435, July.
    2. Christensen, Kim & Kinnebrock, Silja & Podolskij, Mark, 2010. "Pre-averaging estimators of the ex-post covariance matrix in noisy diffusion models with non-synchronous data," Journal of Econometrics, Elsevier, vol. 159(1), pages 116-133, November.
    3. Yacine Aït-Sahalia & Jean Jacod, 2014. "High-Frequency Financial Econometrics," Economics Books, Princeton University Press, edition 1, number 10261.
    4. Omar El Euch & Mathieu Rosenbaum, 2019. "The characteristic function of rough Heston models," Mathematical Finance, Wiley Blackwell, vol. 29(1), pages 3-38, January.
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