Advanced search
Publication Cover
Communications in Statistics - Theory and Methods Volume 49, 2020 - Issue 22
Submit an article Journal homepage
121
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

Signed compound poisson integer-valued GARCH processes

Esmeralda GonçalvesCMUC, Department of Mathematics, University of Coimbra, Coimbra, PortugalCorrespondence[email protected]
ORCID Iconhttp://orcid.org/0000-0002-2317-5183View further author information
ORCID Icon &
Nazaré Mendes-LopesCMUC, Department of Mathematics, University of Coimbra, Coimbra, PortugalORCID Iconhttp://orcid.org/0000-0002-3315-4204View further author information
ORCID Icon
Pages 5468-5492 | Received 17 Oct 2018, Accepted 10 May 2019, Published online: 29 May 2019

References

  • Abramowitz, M., I. Stegun. (eds.). 1965. Handbook of mathematical functions. New York: Dover Publications, Inc.
  • Alomani, G., A. Alzaid, and M. Omair. 2018. A Skellam INGARCH model. Brazilian Journal of Probability and Statistics 32 (1):200–14. doi:10.1214/16-BJPS338.
  • Cui, Y., and F. Zhu. 2018. A new bivariate integer-valued GARCH model allowing for negative cross-correlation. Test 27 (2):428–52. doi:10.1007/s11749-017-0552-4.
  • Ferland, R., A. Latour, and D. Oraichi. 2006. Integer-valued GARCH process. Journal of Time Series Analysis 27 (6):923–42. doi:10.1111/j.1467-9892.2006.00496.x.
  • Gonçalves, E., N. Mendes-Lopes, and F. Silva. 2015. Infinitely divisible distributions in integer-valued GARCH models. Journal of Time Series Analysis 36 (4):503–27. doi:10.1111/jtsa.12112.
  • Gonçalves, E., N. Mendes-Lopes, and F. Silva. 2016. Zero-inflated compound Poisson distributions in integer-valued GARCH models. Statistics 50 (3):558–78. doi:10.1080/02331888.2015.1114622.
  • Halmos, P. 1974. Measure theory. New York: Springer-Verlag.
  • Karlis, D., and I. Ntzoufras. 2006. Bayesian analysis of the differences of count data. Statistics in Medicine 25 (11):1885–905. doi:10.1002/sim.2382.
  • Karlis, D., and I. Ntzoufras. 2008. Bayesian modelling of football outcomes: using the Skellam distribution for the goal difference. IMAJ of Management Mathematics 20 (2):133–45. doi:10.1093/imaman/dpn026.
  • Kim, H. Y., and Y. Park. 2008. A non-stationary integer-valued autoregressive model. Statistical Papers 49 (3):485–502. doi:10.1007/s00362-006-0028-1.
  • Koopman, S.J., R. Lit, A. Lucas. 2014. The Dynamic Skellam Model with Applications. Tinbergen Institute Discussion Paper 14-032/IV/DSF73, Available at SSRN: https://ssrn.com/abstract=2406867 or doi:10.2139/ssrn.2406867.
  • Scotto, M. G., C. H. Weiß, and S. Gouveia. 2015. Thinning-based models in the analysis of integer-valued time series: A review. Statistical Modelling: An International Journal 15 (6):590–618. doi:10.1177/1471082X15584701.
  • Skellam, J. G. 1946. The frequency distribution of the difference between two Poisson variates belonging to different populations. Journal of Royal Statistical Society, A. 109 (3):296. doi:10.2307/2981372.
  • Weiß, C. H. 2009. Modelling time series of counts with overdispersion. Statistical Methods and Applications 18 (4):507–19. doi:10.1007/s10260-008-0108-6.
  • Xu, H.-Y., M. Xie, T. N. Goh, and X. Fu. 2012. A model for integer-valued time series with conditional overdispersion. Computational Statistics and Data Analysis 56 (12):4229–42. doi:10.1016/j.csda.2012.04.011.
  • Zeger, S. L. 1988. A regression model for time series of counts. Biometrika 75 (4):621–9. doi:10.2307/2336303.
  • Zhang, H., D. Wang, and F. Zhu. 2010. Inference for INAR(p) processes with signed generalized power series thinning operator. Journal of Statistical Planning and Inference 140 (3):667–83. doi:10.1016/j.jspi.2009.08.012.
  • Zhang, H., D. Wang, and F. Zhu. 2012. Generalized RCINAR(1) process with signed thinning operator. Communications in Statistics-Theory and Methods 41 (10):1750–70. doi:10.1080/03610926.2010.551452.
  • Zhu, F. 2011. A negative binomial integer-valued GARCH model. Journal of Time Series Analysis 32 (1):54–67. doi:10.1111/j.1467-9892.2010.00684.x.
  • Zhu, F. 2012. Modelling overdispersed or underdispersed count data with generalized Poisson integer-valued GARCH models. Journal of Mathematical Analysis and Applications 389 (1):58–71. doi:10.1016/j.jmaa.2011.11.042.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.