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High frequency principal component analysis based on correlation matrix that is robust to jumps, microstructure noise and asynchronous observation times

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  • Chen, Dachuan

Abstract

This paper developed the high frequency estimation for the principal component analysis (PCA) based on correlation matrix. This estimation methodology is robust to jumps, microstructure noise and asynchronous observation times simultaneously, which is enabled by the newly proposed Truncated and Smoothed Two-Scales Realized Volatility (Truncated S-TSRV) estimator. The general framework of our methodology is constructed based on the estimation of realized spectral functions with respect to the spot correlation matrix. A new asymptotic representation for the element-wise estimation error of the spot correlation matrix estimate has been derived, resulting in a new bias correction term which is much more complex than that of the PCA based covariance matrix. Central limit theorem and rate of convergence have been developed for the bias-corrected estimator. The standard error estimator has also been proposed. As the empirical study of our methodology, we have constructed the first eigen-portfolio based on the eigenvector estimate corresponding to the largest eigenvalue in the spot correlation matrix. We regress the returns of first eigen-portfolio against that of the market ETF, which obtained non-significant alpha estimate and significant beta estimate which is very close to one.

Suggested Citation

  • Chen, Dachuan, 2024. "High frequency principal component analysis based on correlation matrix that is robust to jumps, microstructure noise and asynchronous observation times," Journal of Econometrics, Elsevier, vol. 240(1).
    • Handle: RePEc:eee:econom:v:240:y:2024:i:1:s0304407624000472
    DOI: 10.1016/j.jeconom.2024.105701
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    1. Jacod, Jean & Li, Yingying & Mykland, Per A. & Podolskij, Mark & Vetter, Mathias, 2009. "Microstructure noise in the continuous case: The pre-averaging approach," Stochastic Processes and their Applications, Elsevier, vol. 119(7), pages 2249-2276, July.
    2. Billio, Monica & Getmansky, Mila & Lo, Andrew W. & Pelizzon, Loriana, 2012. "Econometric measures of connectedness and systemic risk in the finance and insurance sectors," Journal of Financial Economics, Elsevier, vol. 104(3), pages 535-559.
    3. Zhang, Lan & Mykland, Per A. & Ait-Sahalia, Yacine, 2005. "A Tale of Two Time Scales: Determining Integrated Volatility With Noisy High-Frequency Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1394-1411, December.
    4. Aït-Sahalia, Yacine & Mykland, Per A. & Zhang, Lan, 2011. "Ultra high frequency volatility estimation with dependent microstructure noise," Journal of Econometrics, Elsevier, vol. 160(1), pages 160-175, January.
    5. Aït-Sahalia, Yacine & Xiu, Dacheng, 2017. "Using principal component analysis to estimate a high dimensional factor model with high-frequency data," Journal of Econometrics, Elsevier, vol. 201(2), pages 384-399.
    6. Marco Avellaneda, 2020. "Hierarchical PCA and Applications to Portfolio Management," Remef - Revista Mexicana de Economía y Finanzas Nueva Época REMEF (The Mexican Journal of Economics and Finance), Instituto Mexicano de Ejecutivos de Finanzas, IMEF, vol. 15(1), pages 1-16, Enero - M.
    7. Dominik M. Rösch & Avanidhar Subrahmanyam & Mathijs A. van Dijk, 2017. "The Dynamics of Market Efficiency," The Review of Financial Studies, Society for Financial Studies, vol. 30(4), pages 1151-1187.
    8. Yacine Aït-Sahalia & Jean Jacod, 2014. "High-Frequency Financial Econometrics," Economics Books, Princeton University Press, edition 1, number 10261.
    9. Kollo, T. & Neudecker, H., 1993. "Asymptotics of Eigenvalues and Unit-Length Eigenvectors of Sample Variance and Correlation Matrices," Journal of Multivariate Analysis, Elsevier, vol. 47(2), pages 283-300, November.
    10. Dion Bongaerts & Frank De Jong & Joost Driessen, 2011. "Derivative Pricing with Liquidity Risk: Theory and Evidence from the Credit Default Swap Market," Journal of Finance, American Finance Association, vol. 66(1), pages 203-240, February.
    11. Ekkehart Boehmer & Dan Li & Gideon Saar, 2018. "The Competitive Landscape of High-Frequency Trading Firms," The Review of Financial Studies, Society for Financial Studies, vol. 31(6), pages 2227-2276.
    12. Xin-Bing Kong, 2017. "On the number of common factors with high-frequency data," Biometrika, Biometrika Trust, vol. 104(2), pages 397-410.
    13. Sydney C. Ludvigson & Serena Ng, 2009. "Macro Factors in Bond Risk Premia," The Review of Financial Studies, Society for Financial Studies, vol. 22(12), pages 5027-5067, December.
    14. Dick-Nielsen, Jens & Feldhütter, Peter & Lando, David, 2012. "Corporate bond liquidity before and after the onset of the subprime crisis," Journal of Financial Economics, Elsevier, vol. 103(3), pages 471-492.
    15. Pelger, Markus, 2019. "Large-dimensional factor modeling based on high-frequency observations," Journal of Econometrics, Elsevier, vol. 208(1), pages 23-42.
    16. Dachuan Chen & Per A. Mykland & Lan Zhang, 2020. "The Five Trolls Under the Bridge: Principal Component Analysis With Asynchronous and Noisy High Frequency Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(532), pages 1960-1977, December.
    17. Mykland, Per A. & Zhang, Lan & Chen, Dachuan, 2019. "The algebra of two scales estimation, and the S-TSRV: High frequency estimation that is robust to sampling times," Journal of Econometrics, Elsevier, vol. 208(1), pages 101-119.
    18. Per A. Mykland & Lan Zhang, 2017. "Assessment of Uncertainty in High Frequency Data: The Observed Asymptotic Variance," Econometrica, Econometric Society, vol. 85, pages 197-231, January.
    19. Dai, Chaoxing & Lu, Kun & Xiu, Dacheng, 2019. "Knowing factors or factor loadings, or neither? Evaluating estimators of large covariance matrices with noisy and asynchronous data," Journal of Econometrics, Elsevier, vol. 208(1), pages 43-79.
    20. Bollerslev, Tim & Meddahi, Nour & Nyawa, Serge, 2019. "High-dimensional multivariate realized volatility estimation," Journal of Econometrics, Elsevier, vol. 212(1), pages 116-136.
    21. Fang, C. & Krishnaiah, P. R., 1982. "Asymptotic distributions of functions of the eigenvalues of some random matrices for nonnormal populations," Journal of Multivariate Analysis, Elsevier, vol. 12(1), pages 39-63, March.
    22. Yacine Aït-Sahalia & Dacheng Xiu, 2019. "Principal Component Analysis of High-Frequency Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(525), pages 287-303, January.
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