Time series models with univariate margins in the convolution-closed infinitely divisible class

Journal of Applied Probability

Volumn 33, Issue 3, 1996, Pages 664-677

  Joe, Harry ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

Count data; Infinitely divisible; Negative binomial; Non normal time series

Indexed keywords

EID: 0030511667     PISSN: 00219002     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0021900200100105     Document Type: Article

References (22)

1. AL-OSH, M. A. AND ALY, E. A. A. (1992) First order autoregressive time series with negative binomial and geometric marginals. Commun. Statist. A 21, 2483-2492.
2. AL-OSH, M. A. AND ALZAID, A. A. (1987) First-order integer-valued autoregressive (INAR(1)) process. J. Time Series Anal. 8, 261-275.
3. AL-OSH, M. A. AND ALZAID, A. A. (1991) Binomial autoregressive moving average models. Commun. Statist. Stoch. Models 7, 261-282.
4. AL-OSH, M. A. AND ALZAID, A. A. (1993) Some gamma processes based on the Dirichlet-gamma transformation. Commun. Statist. Stoch. Models 9, 123-143.
5. AL-OSH, M. A. AND ALZAID, A. A. (1994) A class of non-negative time series processes with ARMA structure. J. Appl. Statist. Sci. 1, 313-322.
6. ALZAID, A. A. AND AL-OSH, M. A. (1991) An integer-valued pth order autoregressive structure (INAR(p)) process. J. Appl. Prob. 27, 314-324.
7. ALZAID, A. A. AND AL-OSH, M. A. (1993) Some autoregressive moving average processes with generalized Poisson marginal distributions. Ann. Int. Statist. Math. 45, 223-232.
8. BARNDORFF-NIELSEN, O. E. AND JORGENSEN, B. (1991) Some parametric models on the simplex. J. Multivariate Anal. 39, 106-116.
9. CONSUL, P. C. (1989) Generalized Poisson Distribution: Properties and Applications. Marcel Dekker, New York.
10. JORGENSEN, B. (1986) Some properties of exponential dispersion models. Scand. J. Statist. 13, 187-197.
11. JORGENSEN, B. (1992) Exponential dispersion models and extensions: a review. Int. Statist. Rev. 60, 5-20.
12. LAWLESS, J. (1987) Negative binomial and mixed Poisson regression. Canad. J. Statist. 15, 209-225.
13. LEWIS, P. A. W. (1983) Generating negatively correlated gamma variates using the beta-gamma transform. In Proc. 1983 Winter Simulation Conf. ed. S. Roberts, J. Banks and B. Schmeiser. IEEE Press, New York, pp. 175-176.
14. LEWIS, P. A. W., MCKENZIE, E. AND HUGUS, D. K. (1989) Gamma processes. Commun. Statist. Stoch. Models 5, 1-30.
15. MARSHALL, A. W. AND OLKIN, I. (1985) A family of bivariate distributions generated by the bivariate Bernoulli distribution. J. Amer. Statist. Assoc. 80, 332-338.
16. MCCORMICK, W. P. AND PARK, Y. S. (1992) Asymptotic analysis of extremes from autoregressive negative binomial processes. J. Appl. Prob. 29, 904-920.
17. MCKENZIE, E. (1985) Some simple models for discrete variate time series. Water Resources Bull. 21, 645-650.
18. MCKENZIE, E. (1986) Autoregressive moving-average processes with negative-binomial and geometric marginal distributions. Adv. Appl. Prob. 18, 679-705.
19. MCKENZIE, E. (1988) Some ARMA models for dependent sequences of Poisson counts. Adv. Appl. Prob. 20, 822-835.
20. OLKIN, I., PETKAU, A. J. AND ZIDEK, J. V. (1981) A comparison of n estimators for the binomial distribution. J. Amer. Statist. Assoc. 76, 637-642.
21. TEICHER, H. (1954) On the multivariate Poisson distribution. Skand. Akt. 37, 1-9.
22. ZEGER, S. L. AND LIANG, K.-Y. (1986) Longitudinal data analysis for discrete and continuous outcomes. Biometrics 42, 121-130.