lynx   »   [go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v229y2022i2p363-395.html
   My bibliography  Save this article

Testing the eigenvalue structure of spot and integrated covariance

Author

Listed:
  • Dovonon, Prosper
  • Taamouti, Abderrahim
  • Williams, Julian
Abstract
For vector Itô semimartingale dynamics, we derive the asymptotic distributions of likelihood-ratio-type test statistics for the purpose of identifying the eigenvalue structure of both integrated and spot covariance matrices estimated using high-frequency data. Unlike the existing approaches where the cross-section dimension grows to infinity, our tests do not necessarily require large cross-section and thus allow for a wide range of applications. The tests, however, are based on non-standard asymptotic distributions with many nuisance parameters. Another contribution of this paper consists in proposing a bootstrap method to approximate these asymptotic distributions. While standard bootstrap methods focus on sampling point-wise returns, the proposed method replicates features of the asymptotic approximation of the statistics of interest that guarantee its validity. A Monte Carlo simulation study shows that the bootstrap-based test controls size and has power for even moderate size samples.

Suggested Citation

  • Dovonon, Prosper & Taamouti, Abderrahim & Williams, Julian, 2022. "Testing the eigenvalue structure of spot and integrated covariance," Journal of Econometrics, Elsevier, vol. 229(2), pages 363-395.
    • Handle: RePEc:eee:econom:v:229:y:2022:i:2:p:363-395
    DOI: 10.1016/j.jeconom.2021.02.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407621000579
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jeconom.2021.02.006?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Ang, Andrew & Liu, Jun & Schwarz, Krista, 2020. "Using Stocks or Portfolios in Tests of Factor Models," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 55(3), pages 709-750, May.
    2. Joao Gomes & Leonid Kogan & Lu Zhang, 2004. "Erratum: "Equilibrium Cross Section of Returns"," Journal of Political Economy, University of Chicago Press, vol. 112(3), pages 724-753, June.
    3. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    4. Hounyo, Ulrich & Gonçalves, Sílvia & Meddahi, Nour, 2017. "Bootstrapping Pre-Averaged Realized Volatility Under Market Microstructure Noise," Econometric Theory, Cambridge University Press, vol. 33(4), pages 791-838, August.
    5. Ole E. Barndorff-Nielsen & Neil Shephard, 2004. "Econometric Analysis of Realized Covariation: High Frequency Based Covariance, Regression, and Correlation in Financial Economics," Econometrica, Econometric Society, vol. 72(3), pages 885-925, May.
    6. Ravi Jagannathan & Yong Wang, 2007. "Lazy Investors, Discretionary Consumption, and the Cross‐Section of Stock Returns," Journal of Finance, American Finance Association, vol. 62(4), pages 1623-1661, August.
    7. Seung C. Ahn & Alex R. Horenstein, 2013. "Eigenvalue Ratio Test for the Number of Factors," Econometrica, Econometric Society, vol. 81(3), pages 1203-1227, May.
    8. Dovonon, Prosper & Gonçalves, Sílvia & Meddahi, Nour, 2013. "Bootstrapping realized multivariate volatility measures," Journal of Econometrics, Elsevier, vol. 172(1), pages 49-65.
    9. Michael J. Cooper & Huseyin Gulen & Michael J. Schill, 2008. "Asset Growth and the Cross‐Section of Stock Returns," Journal of Finance, American Finance Association, vol. 63(4), pages 1609-1651, August.
    10. 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.
    11. Chen, Qihui & Fang, Zheng, 2019. "Inference on functionals under first order degeneracy," Journal of Econometrics, Elsevier, vol. 210(2), pages 459-481.
    12. Todorov, Viktor & Bollerslev, Tim, 2010. "Jumps and betas: A new framework for disentangling and estimating systematic risks," Journal of Econometrics, Elsevier, vol. 157(2), pages 220-235, August.
    13. Qihui Chen & Zheng Fang, 2019. "Inference on Functionals under First Order Degeneracy," Papers 1901.04861, arXiv.org.
    14. Yacine Aït-Sahalia & Jean Jacod, 2014. "High-Frequency Financial Econometrics," Economics Books, Princeton University Press, edition 1, number 10261.
    15. Joao Gomes & Leonid Kogan & Lu Zhang, 2003. "Equilibrium Cross Section of Returns," Journal of Political Economy, University of Chicago Press, vol. 111(4), pages 693-732, August.
    16. Magnus, Jan R., 1985. "On Differentiating Eigenvalues and Eigenvectors," Econometric Theory, Cambridge University Press, vol. 1(2), pages 179-191, August.
    17. Hounyo, Ulrich, 2017. "Bootstrapping integrated covariance matrix estimators in noisy jump–diffusion models with non-synchronous trading," Journal of Econometrics, Elsevier, vol. 197(1), pages 130-152.
    18. Pelger, Markus, 2019. "Large-dimensional factor modeling based on high-frequency observations," Journal of Econometrics, Elsevier, vol. 208(1), pages 23-42.
    19. Chamberlain, Gary & Rothschild, Michael, 1983. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," Econometrica, Econometric Society, vol. 51(5), pages 1281-1304, September.
    20. Alexei Onatski, 2010. "Determining the Number of Factors from Empirical Distribution of Eigenvalues," The Review of Economics and Statistics, MIT Press, vol. 92(4), pages 1004-1016, November.
    21. Cochrane, John H, 1996. "A Cross-Sectional Test of an Investment-Based Asset Pricing Model," Journal of Political Economy, University of Chicago Press, vol. 104(3), pages 572-621, June.
    22. Magnus, J.R. & Neudecker, H., 1979. "The commutation matrix : Some properties and applications," Other publications TiSEM d0b1e779-7795-4676-ac98-1, Tilburg University, School of Economics and Management.
    23. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gagliardini, Patrick & Ossola, Elisa & Scaillet, Olivier, 2020. "Estimation of large dimensional conditional factor models in finance," Handbook of Econometrics, in: Steven N. Durlauf & Lars Peter Hansen & James J. Heckman & Rosa L. Matzkin (ed.), Handbook of Econometrics, edition 1, volume 7, chapter 0, pages 219-282, Elsevier.
    2. 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.
    3. Torben G. Andersen & Yi Ding & Viktor Todorov & Seunghyeon Yu, 2025. "The Factor Structure of Jump Risk," Working Papers 202531, University of Macau, Faculty of Business Administration.
    4. Pelger, Markus, 2019. "Large-dimensional factor modeling based on high-frequency observations," Journal of Econometrics, Elsevier, vol. 208(1), pages 23-42.
    5. Barigozzi, Matteo & Cho, Haeran & Fryzlewicz, Piotr, 2018. "Simultaneous multiple change-point and factor analysis for high-dimensional time series," Journal of Econometrics, Elsevier, vol. 206(1), pages 187-225.
    6. Chaieb, Ines & Langlois, Hugues & Scaillet, Olivier, 2021. "Factors and risk premia in individual international stock returns," Journal of Financial Economics, Elsevier, vol. 141(2), pages 669-692.
    7. Alain-Philippe Fortin & Patrick Gagliardini & O. Scaillet, 2022. "Eigenvalue tests for the number of latent factors in short panels," Swiss Finance Institute Research Paper Series 22-81, Swiss Finance Institute.
    8. Alessi, Lucia & Ossola, Elisa & Panzica, Roberto, 2023. "When do investors go green? Evidence from a time-varying asset-pricing model," International Review of Financial Analysis, Elsevier, vol. 90(C).
    9. Choi, Sung Hoon & Kim, Donggyu, 2023. "Large volatility matrix analysis using global and national factor models," Journal of Econometrics, Elsevier, vol. 235(2), pages 1917-1933.
    10. Patrick Gagliardini & Elisa Ossola & Olivier Scaillet, 2016. "Time‐Varying Risk Premium in Large Cross‐Sectional Equity Data Sets," Econometrica, Econometric Society, vol. 84, pages 985-1046, May.
    11. Amit Goyal, 2012. "Empirical cross-sectional asset pricing: a survey," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 26(1), pages 3-38, March.
    12. Lettau, Martin & Pelger, Markus, 2020. "Estimating latent asset-pricing factors," Journal of Econometrics, Elsevier, vol. 218(1), pages 1-31.
    13. Ding, Yi & Li, Yingying & Zheng, Xinghua, 2021. "High dimensional minimum variance portfolio estimation under statistical factor models," Journal of Econometrics, Elsevier, vol. 222(1), pages 502-515.
    14. Gagliardini, Patrick & Ossola, Elisa & Scaillet, Olivier, 2019. "A diagnostic criterion for approximate factor structure," Journal of Econometrics, Elsevier, vol. 212(2), pages 503-521.
    15. repec:gnv:wpaper:unige:76321 is not listed on IDEAS
    16. Gu, Shihao & Kelly, Bryan & Xiu, Dacheng, 2021. "Autoencoder asset pricing models," Journal of Econometrics, Elsevier, vol. 222(1), pages 429-450.
    17. Andreou, Elena & Ghysels, Eric, 2021. "Predicting the VIX and the volatility risk premium: The role of short-run funding spreads Volatility Factors," Journal of Econometrics, Elsevier, vol. 220(2), pages 366-398.
    18. Yu, Long & He, Yong & Zhang, Xinsheng, 2019. "Robust factor number specification for large-dimensional elliptical factor model," Journal of Multivariate Analysis, Elsevier, vol. 174(C).
    19. Markus Pelger, 2020. "Understanding Systematic Risk: A High‐Frequency Approach," Journal of Finance, American Finance Association, vol. 75(4), pages 2179-2220, August.
    20. 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.
    21. Sun, Yucheng & Xu, Wen & Zhang, Chuanhai, 2023. "Identifying latent factors based on high-frequency data," Journal of Econometrics, Elsevier, vol. 233(1), pages 251-270.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;
    ;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G01 - Financial Economics - - General - - - Financial Crises

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:229:y:2022:i:2:p:363-395. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.
    Лучший частный хостинг