Nothing Special   »   [go: up one dir, main page]

skip to main content
10.1145/3523089.3523095acmotherconferencesArticle/Chapter ViewAbstractPublication PagesiccdaConference Proceedingsconference-collections
research-article

3:A SUE-Poisson INARCH(1) Model

Published: 23 May 2022 Publication History

Abstract

This article illustrates the connection between a time series of counts and pure birth processes. The rejection of the Poisson INARCH (1) model is so universal in real applications. A reasonable explanation is that the Poisson process is a pure birth process with constant rates. Typically, the conditional over-, under-, and equidispersed distributions of a time series of counts are related to pure birth processes with unequal (monotonic or non-monotonic) and equal rates. Thus, a new INARCH (1) model with conditional unequal-rate and equal-rate distributions is proposed. This parsimonious model is applied to the time series of strike counts and yields considerably better results to the Poisson INARCH (1) model and other conventional models in the literature.

References

[1]
Al-Osh, M.A. and Alzaid, A. A. 1987. First-order integer-valued autoregressive (INAR(1)) process. Journal of Time Series Analysis 8, 3 (May 1987), 261-275. DOI= https://doi.org/10.1111/j.1467-9892.1987.tb00438.x
[2]
Bourguignon, M., Rodrigues, J., and Santos-Neto, M. 2019. Extended Poisson INAR(1) processes with equidispersion, underdispersion and overdispersion. Journal of Applied Statistics 46, 1 (2019), 101–118. DOI= https://doi.org/10.1080/02664763.2018.1458216
[3]
Ferland, R., Latour, A., and Oraichi, D. 2006. Integer-valued GARCH process. Journal of Time Series Analysis 27, 6 (Nov. 2006), 923–942. DOI= https://doi.org/10.1111/j.1467-9892.2006.00496.x
[4]
Fokianos, K. and Fried, R. 2010. Interventions in INGARCH processes. Journal of Time Series Analysis 31, 3 (May 2010), 210–225. DOI= https://doi.org/10.1111/j.1467-9892.2010.00657.x
[5]
Fokianos, K., Rahbek, A., and Tjøstheim, D. 2009. Poisson autoregression. Journal of the American Statistical Association 104, 488 (2009), 1430–1439. DOI= https://doi.org/10.1198/jasa.2009.tm08270
[6]
Gonçalves, E., Mendes-Lopes, N., and Silva, F. 2015. Infinitely divisible distributions in integer-valued GARCH models. Journal of Time Series Analysis 36, 4 (Jul. 2015), 503–527. DOI= https://doi.org/10.1111/jtsa.12112
[7]
Heinen, A. 2003. Modelling time series count data: an autoregressive conditional Poisson model. CORE Discussion Paper 2003/62, University of Louvain, Belgium. DOI= http://dx.doi.org/10.2139/ssrn.1117187 or https://ssrn.com/abstract=1117187
[8]
Huang, J. and Zhu, F. 2021. A new first-order integer-valued autoregressive model with Bell innovations. Entropy 23, 6 (2021), 713. DOI= https://doi.org/10.3390/e23060713
[9]
Jazi, M. A., Jones, G., and Lai, C. 2012. Integer valued AR(1) with geometric innovations. Journal of the Iranian Statistical Society 11, 2 (Nov. 2012), 173–190.
[10]
Jung, R. C., Ronning, G., and Tremayne, A. R. 2005. Estimation in conditional first order autoregression with discrete support. Statistical Papers 46 (Apr. 2005), 195–224.
[11]
McKenzie, E. 1985. Some simple models for discrete variate time series. JAWRA Journal of the American Water Resources Association 21, 4 (Aug. 1985), 645–650. DOI= https://doi.org/10.1111/j.1752-1688.1985.tb05379.x
[12]
Neumann, M. H. 2011. Absolute regularity and ergodicity of Poisson count processes. Bernoulli 17, 4 (Nov. 2011), 1268–1284. DOI= https://doi.org/10.3150/10-BEJ313
[13]
Schweer, S. and Weiß, C. H. 2014. Compound Poisson INAR(1) processes: Stochastic properties and testing for overdispersion. Computational Statistics and Data Analysis 77 (Sep 2014), 267–284. DOI= https://doi.org/10.1016/j.csda.2014.03.005
[14]
Silva, R. B. and Barreto-Souza, W. 2019. Flexible and robust mixed Poisson INGARCH models. Journal of Time Series Analysis 40, 5 (Sep. 2019), 788–814. DOI= https://doi.org/10.1111/jtsa.12459
[15]
Skulpakdee, W., and Hunkrajok, M. 2021. Models based on exponential interarrival times for single-unusual-event count data. arXiv:2104.15087 [stat.AP]. Retrieved from https://arxiv.org/abs/2104.15087
[16]
Skulpakdee, W., and Hunkrajok, M. 2022. Unusual-event processes for count data. SORT-Statistics and Operations Research Transactions. Accepted for publication.
[17]
Weiß, C. H. 2009. Modelling time series of counts with overdispersion. Statistical Methods and Applications 18 (2009), 507–519. DOI= https://doi.org/10.1007/s10260-008-0108-6
[18]
Weiß, C. H. 2010. The INARCH(1) model for overdispersed time series of counts. Communications in Statistics-Simulation and Computation 39, 6 (2010), 1269–1291. DOI= https://doi.org/10.1080/03610918.2010.490317
[19]
Weiß, C. H. 2013. Integer-valued autoregressive models for counts showing underdispersion. Journal of Applied Statistics 40, 9 (2013), 1931–1948. DOI= https://doi.org/10.1080/02664763.2013.800034
[20]
Weiß, C. H. 2018. An Introduction to Discrete-Valued Time Series. John Wiley and Sons Ltd., Hoboken, NJ, USA. Retrieved from https://onlinelibrary.wiley.com/doi/book/10.1002/9781119097013
[21]
Weiß, C. H., Homburg, A., Alwan, L. C., Frahm, G., and Göb, R. 2021. Efficient accounting for estimation uncertainty in coherent forecasting of count processes. Journal of Applied Statistics (2021). DOI= https://doi.org/10.1080/02664763.2021.1887104
[22]
Weiß, C. H., Zhu, F., and Hoshiyar, A. 2022. Softplus INGARCH models. Statistica Sinica. 32, 3 (2022). DOI= https://doi.org/10.5705 /ss.202020.0353
[23]
Xu, H., Xie, M., Goh, T. N., and Fu, X. 2012. A model for integer-valued time series with conditional overdispersion. Computational Statistics and Data Analysis 56, 12 (Dec. 2012), 4229–4242. DOI= https://doi.org/10.1016/j.csda.2012.04.011
[24]
Zhu, F. 2011. A negative binomial integer-valued GARCH model. Journal of Time Series Analysis 32, 1 (Jan. 2011) 54–67. DOI= https://doi.org/10.1111/j.1467-9892.2010.00684.x
[25]
Zhu, F. 2012. Modeling overdispersed or underdispersed count data with generalized Poisson integer-valued GARCH models. Journal of Mathematical Analysis and Applications 389, 1 (May 2012) 58–71. DOI= https://doi.org/10.1016/j.jmaa.2011.11.042
[26]
Zhu, F., Li, Q., and Wang, D. 2010. A mixture integer-valued ARCH model. Journal of Statistical Planning and Inference 140, 7 (July 2010) 2025-2036. DOI= https://doi.org/10.1016/j.jspi.2010.01.037

Cited By

View all
  • (2024)A simple algorithm for computing the probabilities of count models based on pure birth processesComputational Statistics10.1007/s00180-024-01491-4Online publication date: 10-Apr-2024

Recommendations

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

cover image ACM Other conferences
ICCDA '22: Proceedings of the 2022 6th International Conference on Compute and Data Analysis
February 2022
131 pages
ISBN:9781450395472
DOI:10.1145/3523089
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 23 May 2022

Permissions

Request permissions for this article.

Check for updates

Author Tags

  1. Count time series
  2. GARCH
  3. INAR
  4. Overdispersion
  5. Stationarity
  6. Underdispersion

Qualifiers

  • Research-article
  • Research
  • Refereed limited

Conference

ICCDA 2022

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • Downloads (Last 12 months)14
  • Downloads (Last 6 weeks)0
Reflects downloads up to 13 Nov 2024

Other Metrics

Citations

Cited By

View all
  • (2024)A simple algorithm for computing the probabilities of count models based on pure birth processesComputational Statistics10.1007/s00180-024-01491-4Online publication date: 10-Apr-2024

View Options

Get Access

Login options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

HTML Format

View this article in HTML Format.

HTML Format

Media

Figures

Other

Tables

Share

Share

Share this Publication link

Share on social media