IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v41y1999i2p131-137.html
   My bibliography  Save this article

The correlation structure of the sample autocovariance function for a particular class of time series with elliptically contoured distribution

Author

Listed:
  • Genton, Marc G.

Abstract

In the context of time series, the classical estimator of the autocovariance function can be written as a quadratic form of the observations. If data have an elliptically contoured distribution with constant mean, then the correlation between the sample autocovariance function at two different lags is a function of the time design matrix and the covariance matrix of the process. When data have a regular support, an explicit formula for this correlation is available for a particular family of covariance matrices. Surprisingly, this correlation structure is exactly the same as the one for a Gaussian white noise.

Suggested Citation

  • Genton, Marc G., 1999. "The correlation structure of the sample autocovariance function for a particular class of time series with elliptically contoured distribution," Statistics & Probability Letters, Elsevier, vol. 41(2), pages 131-137, January.
    • Handle: RePEc:eee:stapro:v:41:y:1999:i:2:p:131-137
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(98)00129-1
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Dufour, Jean-Marie & Roy, Roch, 1985. "Some robust exact results on sample autocorrelations and tests of randomness," Journal of Econometrics, Elsevier, vol. 29(3), pages 257-273, September.
    2. Oliver D. Anderson & Zhao‐Guo Chen, 1996. "Higher Order Moments Of Sample Autocovariances And Sample Autocorrelations From An Independent Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 17(4), pages 323-331, July.
    3. De Gooijer, Jan G., 1980. "Exact moments of the sample autocorrelations from series generated by general arima processes of order (p, d, q), d=0 or 1," Journal of Econometrics, Elsevier, vol. 14(3), pages 365-379, December.
    4. Oliver D. Anderson, 1993. "Exact General‐Lag Serial Correlation Moments And Approximate Low‐Lag Partial Correlation Moments For Gaussian White Noise," Journal of Time Series Analysis, Wiley Blackwell, vol. 14(6), pages 551-574, November.
    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. Genton, Marc G. & He, Li & Liu, Xiangwei, 2001. "Moments of skew-normal random vectors and their quadratic forms," Statistics & Probability Letters, Elsevier, vol. 51(4), pages 319-325, February.
    2. Kim, Hyoung-Moon, 2008. "A note on scale mixtures of skew normal distribution," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1694-1701, September.
    3. Genton, Mark G. & Ruiz-Gazen, Anne, 2009. "Visualizing Influential Observations in Dependent Data," TSE Working Papers 09-051, Toulouse School of Economics (TSE).
    4. Genton, Marc G. & Gorsich, David J., 2002. "Nonparametric variogram and covariogram estimation with Fourier-Bessel matrices," Computational Statistics & Data Analysis, Elsevier, vol. 41(1), pages 47-57, November.

    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. Paolella, Marc S., 2003. "Computing moments of ratios of quadratic forms in normal variables," Computational Statistics & Data Analysis, Elsevier, vol. 42(3), pages 313-331, March.
    2. Kim, Hyoung-Moon, 2008. "A note on scale mixtures of skew normal distribution," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1694-1701, September.
    3. Kan, Raymond & Wang, Xiaolu, 2010. "On the distribution of the sample autocorrelation coefficients," Journal of Econometrics, Elsevier, vol. 154(2), pages 101-121, February.
    4. Palm, F.C. & Sneek, J.M., 1981. "Some econometric applications of the exact distribution of the ratio of two quadratic forms in normal variates," Serie Research Memoranda 0018, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    5. Hallin, Marc & La Vecchia, Davide, 2020. "A Simple R-estimation method for semiparametric duration models," Journal of Econometrics, Elsevier, vol. 218(2), pages 736-749.
    6. Dufour, Jean-Marie & Farhat, Abdeljelil & Hallin, Marc, 2006. "Distribution-free bounds for serial correlation coefficients in heteroskedastic symmetric time series," Journal of Econometrics, Elsevier, vol. 130(1), pages 123-142, January.
    7. Günter Coenen, 2005. "Asymptotic confidence bands for the estimated autocovariance and autocorrelation functions of vector autoregressive models," Empirical Economics, Springer, vol. 30(1), pages 65-75, January.
    8. Hillier, Grant & Kan, Raymond & Wang, Xiaolu, 2009. "Computationally Efficient Recursions For Top-Order Invariant Polynomials With Applications," Econometric Theory, Cambridge University Press, vol. 25(1), pages 211-242, February.
    9. Joanna Olbryś & Elżbieta Majewska, 2014. "Implications of market frictions: serial correlations in indexes on the emerging stock markets in Central and Eastern Europe," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 24(1), pages 51-70.
    10. Kazutaka Kurasawa, 2016. "Policy Uncertainty and Foreign Exchange Rates: The DCC-GARCH Model of the US / Japanese Foreign Exchange Rate," International Journal of Economic Sciences, International Institute of Social and Economic Sciences, vol. 5(4), pages 1-19, December.
    11. Boudoukh, Jacob & Israel, Ronen & Richardson, Matthew, 2022. "Biases in long-horizon predictive regressions," Journal of Financial Economics, Elsevier, vol. 145(3), pages 937-969.
    12. Sneek, J.M. & Smits, J., 1990. "An approximation to the distribution of quadratic forms in many normal variables," Serie Research Memoranda 0049, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    13. Lo, Andrew W. & MacKinlay, A. Craig, 1989. "The size and power of the variance ratio test in finite samples : A Monte Carlo investigation," Journal of Econometrics, Elsevier, vol. 40(2), pages 203-238, February.
    14. Wang, Xuqin & Li, Muyi, 2023. "Bootstrapping the transformed goodness-of-fit test on heavy-tailed GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 184(C).
    15. Luca Bagnato & Lucio De Capitani & Antonio Punzo, 2014. "Testing Serial Independence via Density-Based Measures of Divergence," Methodology and Computing in Applied Probability, Springer, vol. 16(3), pages 627-641, September.
    16. Andy Kwan & Ah-Boon Sim & Yangru Wu, 2005. "On the size and power of normalized autocorrelation coefficients," Applied Financial Economics, Taylor & Francis Journals, vol. 15(1), pages 1-11.
    17. Tsay, Ruey S., 2020. "Testing serial correlations in high-dimensional time series via extreme value theory," Journal of Econometrics, Elsevier, vol. 216(1), pages 106-117.
    18. Neha Seth & Laxmidhar Panda, 2020. "Time-varying Correlation Between Indian Equity Market and Selected Asian and US Stock Markets," Global Business Review, International Management Institute, vol. 21(6), pages 1354-1375, December.
    19. A. C. C. Kwan, 2003. "Sample partial autocorrelations and portmanteau tests for randomness," Applied Economics Letters, Taylor & Francis Journals, vol. 10(10), pages 605-609.
    20. Frédéric Jouneau-Sion & Olivier Torrès, 2014. "In Fisher’s net : exact F-tests in semi-parametric models with exchangeable errors," Working Papers 1422, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.

    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:stapro:v:41:y:1999:i:2:p:131-137. 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/wps/find/journaldescription.cws_home/622892/description#description .

    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.