IDEAS home Printed from
   My bibliography  Save this paper

Note on Integer-Valued Bilinear Time Series Models


  • Drost, F.C.

    (Tilburg University, Center For Economic Research)

  • van den Akker, R.

    (Tilburg University, Center For Economic Research)

  • Werker, B.J.M.

    (Tilburg University, Center For Economic Research)


Summary. This note reconsiders the nonnegative integer-valued bilinear processes introduced by Doukhan, Latour, and Oraichi (2006). Using a hidden Markov argument, we extend their result of the existence of a stationary solution for the INBL(1,0,1,1) process to the class of superdiagonal INBL(p; q; m; n) models. Our approach also yields improved parameter restrictions for several moment conditions compared to the ones in Doukhan, Latour, and Oraichi (2006).

Suggested Citation

  • Drost, F.C. & van den Akker, R. & Werker, B.J.M., 2007. "Note on Integer-Valued Bilinear Time Series Models," Discussion Paper 2007-47, Tilburg University, Center for Economic Research.
  • Handle: RePEc:tiu:tiucen:4eb72bc4-4b8b-45a9-b97c-7c32a52fabe9

    Download full text from publisher

    File URL:
    Download Restriction: no

    Other versions of this item:


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

    Cited by:

    1. Segers, J.J.J. & van den Akker, R. & Werker, B.J.M., 2008. "Improving Upon the Marginal Empirical Distribution Functions when the Copula is Known," Discussion Paper 2008-40, Tilburg University, Center for Economic Research.
    2. Feike C. Drost & Ramon Van Den Akker & Bas J. M. Werker, 2008. "Local asymptotic normality and efficient estimation for INAR(p) models," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(5), pages 783-801, September.
    3. Dag Tjøstheim, 2012. "Some recent theory for autoregressive count time series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(3), pages 413-438, September.
    4. E. Gonçalves & N. Mendes-Lopes & F. Silva, 2015. "Infinitely Divisible Distributions in Integer-Valued Garch Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(4), pages 503-527, July.
    5. repec:tiu:tiutis:6b90fe6f-4de9-4192-9f4d-99ae9220af75 is not listed on IDEAS
    6. Drost, F.C. & van den Akker, R. & Werker, B.J.M., 2009. "The asymptotic structure of nearly unstable non negative integer-valued AR(1) models," Other publications TiSEM ac0494ae-7a32-43ca-b5b4-d, Tilburg University, School of Economics and Management.
    7. Doukhan, Paul & Fokianos, Konstantinos & Li, Xiaoyin, 2012. "On weak dependence conditions: The case of discrete valued processes," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1941-1948.

    More about this item


    count data; integer-valued time series; bilinear model;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes


    Access and download statistics


    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:tiu:tiucen:4eb72bc4-4b8b-45a9-b97c-7c32a52fabe9. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Richard Broekman). General contact details of provider: .

    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.

    We have no references for this item. You can help adding them by using 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.