Some recent theory for autoregressive count time series
In this paper an overview is given over recent theoretical developments in autoregressive count time series. The focus is on generalized autoregressive models where the autoregressive structure is incorporated via a link function. Starting from an ordinary autoregressive model the difficulties in extending standard theory of statistical inference to count time series are highlighted. Special attention is given to the issues of ergodicity and asymptotic theory of estimation. Two main approaches are mentioned, a perturbation approach and the use of a weak dependence concept. The main emphasis is on the former. Linear as well as log-linear and nonlinear models are treated. It is argued that the developed theory forms a necessary basis for modelling and application of these count time series. The setting of the paper is one of simple models and conditional distributions of Poisson type. But it is claimed that the framework is general enough to handle many extensions with an accompanying flexibility in applications of these models. Copyright Sociedad de Estadística e Investigación Operativa 2012
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 21 (2012)
Issue (Month): 3 (September)
|Contact details of provider:|| Web page: http://www.springer.com|
Web page: http://www.seio.es/
|Order Information:||Web: http://www.springer.com/statistics/journal/11749/PS2|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Drost, F.C. & van den Akker, R. & Werker, B.J.M., 2007.
"Note on Integer-Valued Bilinear Time Series Models,"
2007-47, Tilburg University, Center for Economic Research.
- Drost, Feike C. & van den Akker, Ramon & Werker, Bas J.M., 2008. "Note on integer-valued bilinear time series models," Statistics & Probability Letters, Elsevier, vol. 78(8), pages 992-996, June.
- Feike C. Drost & Ramon van den Akker & Bas J. M. Werker, 2009. "Efficient estimation of auto-regression parameters and innovation distributions for semiparametric integer-valued AR("p") models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 467-485.
- Brendan P.M. McCabe & Gael M. Martin & David Harris, 2009. "Optimal Probabilistic Forecasts for Counts," Monash Econometrics and Business Statistics Working Papers 7/09, Monash University, Department of Econometrics and Business Statistics.
- Jensen, S ren Tolver & Rahbek, Anders, 2004. "Asymptotic Inference For Nonstationary Garch," Econometric Theory, Cambridge University Press, vol. 20(06), pages 1203-1226, December.
- HEINEN, Andréas, 2003.
"Modelling time series count data: an autoregressive conditional Poisson model,"
CORE Discussion Papers
2003062, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Heinen, Andreas, 2003. "Modelling Time Series Count Data: An Autoregressive Conditional Poisson Model," MPRA Paper 8113, University Library of Munich, Germany.
- Chao Wang & Wai Keung Li, 2011. "On the autopersistence functions and the autopersistence graphs of binary autoregressive time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(6), pages 639-646, November.
- Konstantinos Fokianos & Dag Tjøstheim, 2012. "Nonlinear Poisson autoregression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(6), pages 1205-1225, December.
- René Ferland & Alain Latour & Driss Oraichi, 2006. "Integer-Valued GARCH Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(6), pages 923-942, November.
- Hans Jensen, 2004. "Review Essay," Review of Social Economy, Taylor & Francis Journals, vol. 62(1), pages 101-112.
- Fokianos, Konstantinos & Tjøstheim, Dag, 2011. "Log-linear Poisson autoregression," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 563-578, March.
- Jung, Robert C. & Liesenfeld, Roman & Richard, Jean-FranÃ§ois, 2011.
"Dynamic Factor Models for Multivariate Count Data: An Application to Stock-Market Trading Activity,"
Journal of Business & Economic Statistics,
American Statistical Association, vol. 29(1), pages 73-85.
- Jung, Robert & Liesenfeld, Roman & Richard, Jean-François, 2008. "Dynamic Factor Models for Multivariate Count Data: An Application to Stock-Market Trading Activity," Economics Working Papers 2008,12, Christian-Albrechts-University of Kiel, Department of Economics.
- Christian Weiß, 2008. "Thinning operations for modeling time series of counts—a survey," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 92(3), pages 319-341, August.
- Mika Meitz & Pentti Saikkonen, 2007.
"Ergodicity, mixing, and existence of moments of a class of Markov models with applications to GARCH and ACD models,"
Economics Series Working Papers
327, University of Oxford, Department of Economics.
- Meitz, Mika & Saikkonen, Pentti, 2008. "Ergodicity, Mixing, And Existence Of Moments Of A Class Of Markov Models With Applications To Garch And Acd Models," Econometric Theory, Cambridge University Press, vol. 24(05), pages 1291-1320, October.
- Meitz, Mika & Saikkonen, Pentti, 2004. "Ergodicity, mixing, and existence of moments of a class of Markov models with applications to GARCH and ACD models," SSE/EFI Working Paper Series in Economics and Finance 573, Stockholm School of Economics, revised 20 Apr 2007.
- 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.
- Doukhan, Paul & Louhichi, Sana, 1999. "A new weak dependence condition and applications to moment inequalities," Stochastic Processes and their Applications, Elsevier, vol. 84(2), pages 313-342, December.
- Richard A. Davis, 2003. "Observation-driven models for Poisson counts," Biometrika, Biometrika Trust, vol. 90(4), pages 777-790, December.
- Jung, Robert C. & Kukuk, Martin & Liesenfeld, Roman, 2006. "Time series of count data: modeling, estimation and diagnostics," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2350-2364, December.
- Konstantinos Fokianos & Benjamin Kedem, 2004. "Partial Likelihood Inference For Time Series Following Generalized Linear Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(2), pages 173-197, 03.
- Heinen, Andreas & Rengifo, Erick, 2007. "Multivariate autoregressive modeling of time series count data using copulas," Journal of Empirical Finance, Elsevier, vol. 14(4), pages 564-583, September.
- Konstantinos Fokianos & Roland Fried, 2010. "Interventions in INGARCH processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(3), pages 210-225, 05.
- Yunwei Cui & Robert Lund, 2009. "A new look at time series of counts," Biometrika, Biometrika Trust, vol. 96(4), pages 781-792.
- Sandmann, Gleb & Koopman, Siem Jan, 1998. "Estimation of stochastic volatility models via Monte Carlo maximum likelihood," Journal of Econometrics, Elsevier, vol. 87(2), pages 271-301, September.
When requesting a correction, please mention this item's handle: RePEc:spr:testjl:v:21:y:2012:i:3:p:413-438. 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: (Sonal Shukla)or (Rebekah McClure)
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 references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link 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 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.