IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v194y2016i2p231-241.html
   My bibliography  Save this article

Copula structured M4 processes with application to high-frequency financial data

Author

Listed:
  • Zhang, Zhengjun
  • Zhu, Bin

Abstract

Statistical applications of classical parametric max-stable processes are still sparse mostly due to lack of (1) efficiency of statistical estimation of many parameters in the processes, (2) flexibility of concurrently modeling asymptotic independence and asymptotic dependence among variables, and (3) capability of fitting real data directly. This paper studies a more flexible model, i.e. a class of copula structured M4 (multivariate maxima and moving maxima) processes, and hence CSM4 for short. CSM4 processes are constructed by incorporating sparse random coefficients and structured extreme value copulas in asymptotically (in)dependent M4 (AIM4) processes. It is shown that the new model overcomes all of the aforementioned three constraints. The paper illustrates new features and advantages of the CSM4 model using simulated examples and real data of intra-daily maxima of high-frequency financial time series. The paper also studies probabilistic properties of the proposed model, and its statistical inference.

Suggested Citation

  • Zhang, Zhengjun & Zhu, Bin, 2016. "Copula structured M4 processes with application to high-frequency financial data," Journal of Econometrics, Elsevier, vol. 194(2), pages 231-241.
    • Handle: RePEc:eee:econom:v:194:y:2016:i:2:p:231-241
    DOI: 10.1016/j.jeconom.2016.05.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407616300938
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jeconom.2016.05.004?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. Zhang, Zhengjun & Huang, James, 2006. "Extremal financial risk models and portfolio evaluation," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2313-2338, December.
    3. Hall, Peter & Peng, Liang & Yao, Qiwei, 2002. "Moving-maximum models for extrema of time series," LSE Research Online Documents on Economics 6084, London School of Economics and Political Science, LSE Library.
    4. Aït-Sahalia, Yacine & Fan, Jianqing & Xiu, Dacheng, 2010. "High-Frequency Covariance Estimates With Noisy and Asynchronous Financial Data," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1504-1517.
    5. Whitney K. Newey & Kenneth D. West, 1994. "Automatic Lag Selection in Covariance Matrix Estimation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(4), pages 631-653.
    6. Härdle, Wolfgang Karl & Hautsch, Nikolaus & Pigorsch, Uta, 2008. "Measuring and modeling risk using high-frequency data," SFB 649 Discussion Papers 2008-045, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    7. Masaaki Sibuya, 1959. "Bivariate extreme statistics, I," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 11(2), pages 195-210, June.
    8. Ser-Huang Poon, 2004. "Extreme Value Dependence in Financial Markets: Diagnostics, Models, and Financial Implications," The Review of Financial Studies, Society for Financial Studies, vol. 17(2), pages 581-610.
    9. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    10. Zhengjun Zhang, 2009. "On approximating max-stable processes and constructing extremal copula functions," Statistical Inference for Stochastic Processes, Springer, vol. 12(1), pages 89-114, February.
    11. Fabrizio Laurini & Jonathan Tawn, 2009. "Regular Variation and Extremal Dependence of GARCH Residuals with Application to Market Risk Measures," Econometric Reviews, Taylor & Francis Journals, vol. 28(1-3), pages 146-169.
    12. McNeil, Alexander J. & Frey, Rudiger, 2000. "Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 271-300, November.
    13. Zhou, Bin, 1996. "High-Frequency Data and Volatility in Foreign-Exchange Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 45-52, January.
    14. Anthony W. Ledford & Jonathan A. Tawn, 2003. "Diagnostics for dependence within time series extremes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 521-543, May.
    15. Hsing, Tailen, 1989. "Extreme value theory for multivariate stationary sequences," Journal of Multivariate Analysis, Elsevier, vol. 29(2), pages 274-291, May.
    16. Deheuvels, Paul, 1983. "Point processes and multivariate extreme values," Journal of Multivariate Analysis, Elsevier, vol. 13(2), pages 257-272, June.
    17. Paul Embrechts & Sidney Resnick & Gennady Samorodnitsky, 1999. "Extreme Value Theory as a Risk Management Tool," North American Actuarial Journal, Taylor & Francis Journals, vol. 3(2), pages 30-41.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Zhao, Zifeng & Zhang, Zhengjun & Chen, Rong, 2018. "Modeling maxima with autoregressive conditional Fréchet model," Journal of Econometrics, Elsevier, vol. 207(2), pages 325-351.
    2. Cui, Qiurong & Xu, Yuqing & Zhang, Zhengjun & Chan, Vincent, 2021. "Max-linear regression models with regularization," Journal of Econometrics, Elsevier, vol. 222(1), pages 579-600.
    3. Arnab Chakrabarti & Rituparna Sen, 2023. "Copula Estimation for Nonsynchronous Financial Data," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 116-149, May.

    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. Giacomini, Raffaella & Komunjer, Ivana, 2005. "Evaluation and Combination of Conditional Quantile Forecasts," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 416-431, October.
    2. Zhang, Zhengjun & Shinki, Kazuhiko, 2007. "Extreme co-movements and extreme impacts in high frequency data in finance," Journal of Banking & Finance, Elsevier, vol. 31(5), pages 1399-1415, May.
    3. Marco Rocco, 2011. "Extreme value theory for finance: a survey," Questioni di Economia e Finanza (Occasional Papers) 99, Bank of Italy, Economic Research and International Relations Area.
    4. Torben G. Andersen & Tim Bollerslev & Peter Christoffersen & Francis X. Diebold, 2007. "Practical Volatility and Correlation Modeling for Financial Market Risk Management," NBER Chapters, in: The Risks of Financial Institutions, pages 513-544, National Bureau of Economic Research, Inc.
    5. Zhao, Zifeng & Zhang, Zhengjun & Chen, Rong, 2018. "Modeling maxima with autoregressive conditional Fréchet model," Journal of Econometrics, Elsevier, vol. 207(2), pages 325-351.
    6. Härdle, Wolfgang & Horowitz, Joel L. & Kreiss, Jens-Peter, 2001. "Bootstrap methods for time series," SFB 373 Discussion Papers 2001,59, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    7. West, Kenneth D., 2006. "Forecast Evaluation," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 3, pages 99-134, Elsevier.
    8. Helene Hamisultane, 2010. "Utility-based pricing of weather derivatives," The European Journal of Finance, Taylor & Francis Journals, vol. 16(6), pages 503-525.
    9. Jushan Bai & Sung Hoon Choi & Yuan Liao, 2021. "Feasible generalized least squares for panel data with cross-sectional and serial correlations," Empirical Economics, Springer, vol. 60(1), pages 309-326, January.
    10. Hussain, Saiful Izzuan & Li, Steven, 2018. "The dependence structure between Chinese and other major stock markets using extreme values and copulas," International Review of Economics & Finance, Elsevier, vol. 56(C), pages 421-437.
    11. Hirukawa, Masayuki, 2023. "Robust Covariance Matrix Estimation in Time Series: A Review," Econometrics and Statistics, Elsevier, vol. 27(C), pages 36-61.
    12. Clark, Todd & McCracken, Michael, 2013. "Advances in Forecast Evaluation," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 1107-1201, Elsevier.
    13. Giray Gozgor, 2012. "Inflation Targeting and Monetary Policy Rules: Further Evidence from the Case of Turkey," Journal of Applied Finance & Banking, SCIENPRESS Ltd, vol. 2(5), pages 1-7.
    14. Todd E. Clark & Kenneth D. West, 2005. "Using Out-of-Sample Mean Squared Prediction Errors to Test the Martingale Difference," NBER Technical Working Papers 0305, National Bureau of Economic Research, Inc.
    15. Issler, João Victor & Soares, Ana Flávia, 2019. "Central Bank credibility and inflation expectations: a microfounded forecasting approach," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 812, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    16. Lee, Wei-Ming & Kuan, Chung-Ming & Hsu, Yu-Chin, 2014. "Testing over-identifying restrictions without consistent estimation of the asymptotic covariance matrix," Journal of Econometrics, Elsevier, vol. 181(2), pages 181-193.
    17. Politis, D N, 2009. "Higher-Order Accurate, Positive Semi-definite Estimation of Large-Sample Covariance and Spectral Density Matrices," University of California at San Diego, Economics Working Paper Series qt66w826hz, Department of Economics, UC San Diego.
    18. Alastair R. Hall, 2015. "Econometricians Have Their Moments: GMM at 32," The Economic Record, The Economic Society of Australia, vol. 91(S1), pages 1-24, June.
    19. Kiefer, Nicholas M. & Vogelsang, Timothy J., 2005. "A New Asymptotic Theory For Heteroskedasticity-Autocorrelation Robust Tests," Econometric Theory, Cambridge University Press, vol. 21(6), pages 1130-1164, December.
    20. Politis, Dimitris, 2005. "Higher-order accurate, positive semi-definite estimation of large-sample covariance and spectral density matrices," University of California at San Diego, Economics Working Paper Series qt7qg2m9rz, Department of Economics, UC San Diego.

    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:194:y:2016:i:2:p:231-241. 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.