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Note on integer-valued bilinear time series models

Author

Listed:
  • Drost, F.C.

    (Tilburg University, School of Economics and Management)

  • van den Akker, R.

    (Tilburg University, School of Economics and Management)

  • Werker, B.J.M.

    (Tilburg University, School of Economics and Management)

Abstract

This note reconsiders the nonnegative integer-valued bilinear processes introduced by Doukhan et al. [Doukhan, P., Latour, A., Oraichi, D., 2006. A simple integer-valued bilinear time series model. Adv. Appl. Prob. 38, 559-578]. 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 models. Our approach also yields improved parameter restrictions for several moment conditions compared to the ones in [Doukhan, P., Latour, A., Oraichi, D., 2006. A simple integer-valued bilinear time series model. Adv. Appl. Prob. 38, 559-578].
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Drost, F.C. & van den Akker, R. & Werker, B.J.M., 2008. "Note on integer-valued bilinear time series models," Other publications TiSEM aaf4f3fe-f141-4784-89b5-0, Tilburg University, School of Economics and Management.
  • Handle: RePEc:tiu:tiutis:aaf4f3fe-f141-4784-89b5-0d5ccd3e983f
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    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. 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.
    6. 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

    JEL classification:

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

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