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Some recent progress in count time series. (English) Zbl 1291.62164

Summary: We review some regression models for the analysis of count time series. These models have been the focus of several investigations over the last years, but only recently simple conditions for stationarity and ergodicity were worked out in detail. This advancement makes possible the development of the maximum-likelihood estimation theory under minimal assumptions.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62J12 Generalized linear models (logistic models)

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References:

[1] DOI: 10.1016/0304-4076(86)90063-1 · Zbl 0616.62119
[2] McCullagh P., Generalized Linear Models, 2. ed. (1989) · Zbl 0744.62098
[3] DOI: 10.1002/0471266981
[4] DOI: 10.1111/j.1467-9892.1987.tb00438.x · Zbl 0617.62096
[5] DOI: 10.1111/j.1467-9892.1991.tb00073.x · Zbl 0727.62084
[6] Joe H., Multivariate Models and Dependence Concepts (1997) · Zbl 0990.62517
[7] DOI: 10.1111/1467-9892.00102 · Zbl 1127.62402
[8] DOI: 10.1239/aap/1151337085 · Zbl 1096.62082
[9] DOI: 10.1111/j.1467-9892.2008.00590.x · Zbl 1198.62090
[10] DOI: 10.1111/j.1467-9868.2008.00687.x · Zbl 1248.62147
[11] McKenzie E., Stochastic Processes: Modelling and Simulation, Handbook of Statist 21 pp 573– (2003)
[12] DOI: 10.1007/s10182-008-0072-3
[13] Cox D. R., Scand. J. Statist. 8 pp 93– (1981)
[14] DOI: 10.1093/biomet/75.4.621 · Zbl 0653.62064
[15] DOI: 10.2307/1391639
[16] MacDonald I. L., Hidden Markov and Other Models for Discrete-valued Time Series (1997) · Zbl 0868.60036
[17] DOI: 10.1093/biomet/asp029 · Zbl 1170.62062
[18] DOI: 10.1093/biomet/asp057 · Zbl 1179.62116
[19] DOI: 10.1007/978-1-4419-0320-4 · Zbl 0709.62080
[20] DOI: 10.2307/2531732 · Zbl 0715.62166
[21] DOI: 10.2307/2533393 · Zbl 0825.62606
[22] DOI: 10.2307/2669519
[23] DOI: 10.1111/1467-9469.00260 · Zbl 1010.62080
[24] Fahrmeir L., Multivariate Statistical Modelling Based on Generalized Linear Models, 2. ed. (2001) · Zbl 0980.62052
[25] DOI: 10.1093/biomet/90.4.777 · Zbl 1436.62418
[26] DOI: 10.1046/j.0143-9782.2003.00344.x · Zbl 1051.62073
[27] DOI: 10.1016/j.csda.2006.08.001 · Zbl 1157.62492
[28] Davis, R. A., Wang, Y. and Dunsmuir, W. T.M. 1999. ”Modelling time series of count data”. InAsymptotics, Nonparametric & Time Series, Edited by: Ghosh, S. 63–114. New York: Marcel Dekker. · Zbl 1069.62540
[29] Jørgensen B., The Theory of Dispersion Models (1997) · Zbl 0928.62052
[30] Zhu F., J. Time Series Anal. (2011)
[31] DOI: 10.1214/aos/1176349844 · Zbl 0603.62032
[32] Slud E. V., Statist. Sinica 4 pp 89– (1994)
[33] DOI: 10.1006/jmva.1998.1765 · Zbl 0919.62105
[34] DOI: 10.1198/jasa.2009.tm08270 · Zbl 1205.62130
[35] Zhu F., Metrika (2009)
[36] Rydberg T. H., Nonlinear and Nonstationary Signal Processing pp 217– (2000)
[37] Streett, S. 2000. ”Some observation driven models for time series of counts”. Colorado State University, Department of Statistics. Ph.D. thesis
[38] Heinen, A. 2003. ”Modelling time series count data: An autoregressive conditional poisson model”. Germany: University Library of Munich. Tech. Rep. MPRA Paper 8113 Available athttp://mpra.ub.uni-muenchen.de/8113/
[39] DOI: 10.1111/j.1467-9892.2006.00496.x · Zbl 1150.62046
[40] Fokianos K., J. Multivariate Anal (2011)
[41] DOI: 10.1093/biomet/68.1.189 · Zbl 0462.62070
[42] Teräsvirta T., Nonlinear Econometric Modelling (2011)
[43] Tong H., Nonlinear Time Series:A Dynamical System Approach (1990)
[44] Fan J., Nonlinear Time Series (2003)
[45] Neumann M., Bernoulli (2010)
[46] DOI: 10.1016/S0304-4149(99)00055-1 · Zbl 0996.60020
[47] Dedecker J., Weak Dependence: With Examples and Applications (2007)
[48] Heyde C. C., Quasi-Likelihood and its Applications: A General Approach to Optimal Parameter Estimation (1997) · Zbl 0879.62076
[49] DOI: 10.3150/bj/1068128975 · Zbl 1064.62094
[50] DOI: 10.1007/s11009-005-1480-4 · Zbl 1078.62091
[51] Cox D. R., Biometrika 62 pp 69– (1975)
[52] Billingsley P., Statistical Inference for Markov Processes (1961) · Zbl 0106.34201
[53] Meyn S. P., Markov Chains and Stochastic Stability (1993) · Zbl 0925.60001
[54] DOI: 10.2307/2344614
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