Stationary time series models with exponential dispersion model margins

Journal of Applied Probability

Volumn 35, Issue 1, 1998, Pages 78-92

  Jørgensen, Bent ^a   Song, Peter Xue Kun ^b  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

^b YORK UNIVERSITY   (Canada)

Author keywords

Autoregressive process; Convolution closed family; Infinite divisibility; Moving average process of infinite order; Non normal time series; Saddlepoint approximation; Small dispersion asymptotics; Thinning

Indexed keywords

EID: 0032387664     PISSN: 00219002     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0021900200014698     Document Type: Article

References (30)

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. ALZAID, A. A. AND AL-OSH, M. A. (1993). Some autoregressive moving average processes with generalized Poisson marginal distributions. Ann. Inst. Statist. Math. 45, 223-232.
4. BARNDORFF-NIELSEN, O. E. AND JØRGENSEN, B. (1991). Some parametric models on the simplex. J. Multivar. Anal. 39, 106-116.
5. BROCKWELL, P. J. AND DAVIS, R. A. (1987). Time Series: Theory and Methods. Springer, New York.
6. CHUNG, K. L. (1974). Course in Probability Theory. 2nd edn. Academic Press, New York.
7. CONSUL, P. C. (1989). Generalized Poisson Distribution: Properties and Applications. Marcel Dekker, New York.
8. DIMRI, V. (1992). Deconvolution and Inverse Theory. Elsevier, Amsterdam.
9. FELLER, W. (1971). An Introduction to Probability Theory and its Applications. Vol. 2. 2nd edn. Wiley, New York.
10. GAVER, D. P. AND LEWIS, P. A. W. (1980). First-order autoregressive gamma sequences and point processes. Adv. Appl. Prob. 12, 727-745.
11. JACOBS, P. A. AND LEWIS, P. A. W. (1977). A mixed autoregressive-moving average exponential sequence and point process (EARMA 1,1). Adv. Appl. Prob. 9, 87-104.
12. JANSSON, P. A. (1984). Deconvolution with Applications in Spectroscopy. Academic Press, New York.
13. JOE, H. (1996). Time series models with univariate margins in the convolution-closed infinitely divisible class. J. Appl. Prob. 33, 664-677.
14. JØRGENSEN, B. (1986). Some properties of exponential dispersion models. Scand. J. Statist. 13, 187-198.
15. JØRGENSEN, B. (1987). Exponential dispersion models (with discussion). J. Roy. Statist. Soc. B 49, 127-162.
16. JØRGENSEN, B. (1992). Exponential dispersion models and extensions: a review. Int. Statist. Rev. 60, 5-20.
17. JØRGENSEN, B. AND SOUZA, M. P. (1994). Fitting Tweedie's compound Poisson model to insurance claims data. Scand. Act. J. 69-93.
18. JØRGENSEN, B., MARTÍNEZ, J. R. AND TSAO, M. (1994). Asymptotic behaviour of the variance function. Scand. J. Statist. 21, 223-243.
19. JØRGENSEN, B. AND MARTÍNEZ, J. R. (1997). Tauber theory for infinitely divisible variance functions. Bernoulli 3, 213-224.
20. LAWRANCE, A. J. (1982). The innovation distribution of a gamma distributed autoregressive process. Scand. J. Statist. 9, 234-236.
21. LAWRANCE, A. J. AND LEWIS, P. A. W. (1977). An exponential moving average sequence and point process (EMA 1). J. Appl. Prob. 14, 98-113.
22. LETAC, G. AND MORA, M. (1990). Natural real exponential families with cubic variances. Ann. Statist. 18, 1-37.
23. 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.
24. LEWIS, P. A. W., MCKENZIE, E. AND HUGUS, D. K. (1989). Gamma processes. Commun. Statist.-Stoch. Models 5, 1-30.
25. MCCORMICK, W. P. AND PARK, Y. S. (1992). Asymptotic analysis of extremes from autoregressive negative binomial processes. J. Appl. Prob. 29, 904-920.
26. MCKENZIE, E. (1986). Autoregressive moving average processes with negative-binomial and geometric marginal distributions. Adv. Appl. Prob. 18, 679-705.
27. MCKENZIE, E. (1988). Some ARMA models for dependent sequences of Poisson counts. Adv. Appl. Prob. 20, 822-835.
28. MORRIS, C. N. (1982). Natural exponential families with quadratic variance functions. Ann. Statist. 10, 65-80.
29. SESHADRI, V. (1992). General exponential models on the unit simplex and related multivariate inverse Gaussian distributions. Statist. Prob. Lett. 14, 385-391.
30. YANAGIMOTO, T. (1989). The inverse binomial distribution as a statistical model. Commun. Statist. 18, 3625-3633.