IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v72y1997i1p121-143.html
   My bibliography  Save this article

Limited distribution of sample partial autocorrelations: A matrix approach

Author

Listed:
  • Ku, Simon F.

Abstract

We develop a technique for derivation of the asymptotic joint distribution of the sample partial autocorrelations of a process, given the corresponding distribution of sample autocorrelations. No assumption of asymptotic normality is needed. The underlying process need not be stationary. The technique is demonstrated through a detailed study of ARMA (1,1)-like processes, but is applicable to other models. The results extend those of Mills and Seneta (1989) for the AR(1)-like case. The study is motivated by the known relationships and properties, especially is the classical AR(p) case, of population and sample partial autocorrelations.

Suggested Citation

  • Ku, Simon F., 1997. "Limited distribution of sample partial autocorrelations: A matrix approach," Stochastic Processes and their Applications, Elsevier, vol. 72(1), pages 121-143, December.
    • Handle: RePEc:eee:spapps:v:72:y:1997:i:1:p:121-143
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(97)00048-3
    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. Mills, T. M. & Seneta, E., 1989. "Goodness-of-fit for a branching process with immigration using sample partial autocorrelations," Stochastic Processes and their Applications, Elsevier, vol. 33(1), pages 151-161, October.
    2. Byoung Seon Choi, 1991. "On The Asymptotic Distribution Of The Generalized Partial Autocorrelation Function In Autoregressive Moving‐Average Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 12(3), pages 193-205, May.
    3. Simon Ku & Eugene Seneta, 1996. "Quenouille-type theorem on autocorrelations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(4), pages 621-630, December.
    4. Barndorff-Nielsen, O. & Schou, G., 1973. "On the parametrization of autoregressive models by partial autocorrelations," Journal of Multivariate Analysis, Elsevier, vol. 3(4), pages 408-419, December.
    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. Marco Del Negro & Frank Schorfheide, 2009. "Monetary Policy Analysis with Potentially Misspecified Models," American Economic Review, American Economic Association, vol. 99(4), pages 1415-1450, September.
    2. Tianqing Liu & Xiaohui Yuan, 2013. "Random rounded integer-valued autoregressive conditional heteroskedastic process," Statistical Papers, Springer, vol. 54(3), pages 645-683, August.
    3. Tobias Hartl & Roland Jucknewitz, 2022. "Approximate state space modelling of unobserved fractional components," Econometric Reviews, Taylor & Francis Journals, vol. 41(1), pages 75-98, January.
    4. Aruoba, S. BoraÄŸan & Diebold, Francis X. & Scotti, Chiara, 2009. "Real-Time Measurement of Business Conditions," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(4), pages 417-427.
    5. Aldo M. Garay & Francyelle L. Medina & Suelem Torres de Freitas & Víctor H. Lachos, 2024. "Bayesian analysis of linear regression models with autoregressive symmetrical errors and incomplete data," Statistical Papers, Springer, vol. 65(9), pages 5649-5690, December.
    6. Heikki Kauppi, 2008. "Yield-Curve Based Probit Models for Forecasting U.S. Recessions: Stability and Dynamics," Discussion Papers 31, Aboa Centre for Economics.
    7. Gabriele Fiorentini & Enrique Sentana, 2016. "Neglected serial correlation tests in UCARIMA models," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 7(1), pages 121-178, March.
    8. repec:jss:jstsof:28:i02 is not listed on IDEAS
    9. Philippe, Anne, 2006. "Bayesian analysis of autoregressive moving average processes with unknown orders," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1904-1923, December.
    10. Chen, Cathy W.S. & Yu, Tiffany H.K., 2005. "Long-term dependence with asymmetric conditional heteroscedasticity in stock returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 353(C), pages 413-424.
    11. Delle Monache, Davide & Petrella, Ivan, 2017. "Adaptive models and heavy tails with an application to inflation forecasting," International Journal of Forecasting, Elsevier, vol. 33(2), pages 482-501.
    12. Tommaso Proietti & Alessandra Luati, 2013. "The Exponential Model for the Spectrum of a Time Series: Extensions and Applications," CEIS Research Paper 272, Tor Vergata University, CEIS, revised 19 Apr 2013.
    13. Ilya Archakov & Peter Reinhard Hansen & Yiyao Luo, 2024. "A new method for generating random correlation matrices," The Econometrics Journal, Royal Economic Society, vol. 27(2), pages 188-212.
    14. Tommaso Proietti & Alessandro Giovannelli, 2018. "A Durbin–Levinson regularized estimator of high-dimensional autocovariance matrices," Biometrika, Biometrika Trust, vol. 105(4), pages 783-795.
    15. Pötscher, Benedikt M. & Preinerstorfer, David, 2018. "Controlling the size of autocorrelation robust tests," Journal of Econometrics, Elsevier, vol. 207(2), pages 406-431.
    16. Fitzgibbon, L.J., 2006. "On sampling stationary autoregressive model parameters uniformly in r2 value," Statistics & Probability Letters, Elsevier, vol. 76(4), pages 349-352, February.
    17. Jung, Robert C. & Tremayne, A.R., 2006. "Coherent forecasting in integer time series models," International Journal of Forecasting, Elsevier, vol. 22(2), pages 223-238.
    18. Wang, Wan-Lun & Fan, Tsai-Hung, 2012. "Bayesian analysis of multivariate t linear mixed models using a combination of IBF and Gibbs samplers," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 300-310.
    19. Fiorentini, Gabriele & Galesi, Alessandro & Sentana, Enrique, 2018. "A spectral EM algorithm for dynamic factor models," Journal of Econometrics, Elsevier, vol. 205(1), pages 249-279.
    20. Simon Ku & Eugene Seneta, 1996. "Quenouille-type theorem on autocorrelations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(4), pages 621-630, December.
    21. Choi, ByoungSeon, 1997. "A recursive algorithm for solving the spatial Yule-Walker equations of causal spatial AR models," Statistics & Probability Letters, Elsevier, vol. 33(3), pages 241-251, May.

    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:spapps:v:72:y:1997:i:1:p:121-143. 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/505572/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.