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Limiting Spectral Distribution of High-dimensional Hayashi-Yoshida Estimator of Integrated Covariance Matrix

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  • Arnab Chakrabarti
  • Rituparna Sen

Abstract

In this paper, the estimation of the Integrated Covariance matrix from high-frequency data, for high dimensional stock price process, is considered. The Hayashi-Yoshida covolatility estimator is an improvement over Realized covolatility for asynchronous data and works well in low dimensions. However it becomes inconsistent and unreliable in the high dimensional situation. We study the bulk spectrum of this matrix and establish its connection to the spectrum of the true covariance matrix in the limiting case where the dimension goes to infinity. The results are illustrated with simulation studies in finite, but high, dimensional cases. An application to real data with tick-by-tick data on 50 stocks is presented.

Suggested Citation

  • Arnab Chakrabarti & Rituparna Sen, 2022. "Limiting Spectral Distribution of High-dimensional Hayashi-Yoshida Estimator of Integrated Covariance Matrix," Papers 2201.00119, arXiv.org.
    • Handle: RePEc:arx:papers:2201.00119
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    References listed on IDEAS

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    1. G. Bonanno & F. Lillo & R. N. Mantegna, 2001. "High-frequency cross-correlation in a set of stocks," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 96-104.
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    3. Jayaram Muthuswamy & Sudipto Sarkar & Aaron Low & Eric Terry, 2001. "Time variation in the correlation structure of exchange rates: high‐frequency analyses," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 21(2), pages 127-144, February.
    4. Zebedee, Allan A. & Kasch-Haroutounian, Maria, 2009. "A closer look at co-movements among stock returns," Journal of Economics and Business, Elsevier, vol. 61(4), pages 279-294, July.
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