Existence and stochastic structure of a non-negative integer-valued autoregressive process

Journal of Time Series Analysis

Volumn 19, Issue 4, 1998, Pages 439-455

  Latour, Alain ^a  

^a NONE

Author keywords

Autoregressive model; Integer valued time series; Spectral density

Indexed keywords

EID: 0345565915     PISSN: 01439782     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9892.00102     Document Type: Article

References (15)

1. ALZAID, A. and AL-OSH, M. (1990) An integer-valued pth order autoregressive structure (INAR(/?)) process. J. Appl. Probab. 21, 314-24.
2. BROCKWELL, P. and DAVIS, R. (1991) Time Series: Theory and Methods, 2nd Edn. New York: Springer.
3. DION, J.-P., GAUTHIER, G. and LATOUR, A. (1995) Branching processes with immigration and integer-valued times series. SERDICA 21, 123-36.
4. DU, J.-G. and LI, Y. (1991) The integer-valued autoregressive (INAR(p)) model. J. Time Ser. Anal. 12, 129-42.
5. FINKBEINER II, D. T. (1978) Introduction to Matrices and Linear Transformations. San Francisco, CA: W. H. Freeman.
6. FRANKE, J. and SELIGMANN, T. (1993) Conditional maximum likelihood estimates for INAR(1) processes and their application to modelling epileptic seizure counts. In Developments in Time Series Analysis (ed. T. S. Rao). New York: Chapman and Hall.
7. GAUTHIER, G. (1991) Modèle de type autorégressif pour les séries chronologiques à valeurs entières non négatives. Master's thesis, Département de mathématiques et d'informatique, Université du Québec à Montréal.
8. _ and LATOUR, A. (1994) Convergence forte des estimateurs des paramètres d'un processus GENAR(p). Ann. Sci. Math. Québec 18, 49-71.
9. HALL, P. and HEYDE, C. (1980) Martingale Limit Theory and Its Application. New York: Academic Press.
10. HEYDE, C. and SENETA, E. (1972) Estimation theory for growth and immigration rates in a multiplicative process. J. Appl. Probab. 9, 235-56.
11. KEDEM, B. and CHIU, L. (1987) On the log normality of rain rate. Proc. Natl Acad. Sci. USA 84, 901-5.
12. KLIMKO, L. and NELSON, P. (1978) On conditional least squares estimation for stochastic processes. Ann. Stat. 6, 629-42.
13. SENETA, E. (1973) Non-negative Matrices. London: George Allen & Unwin.
14. STEUTEL, F. and VAN HARN, K. (1979) Discrete analogues of self-decomposability and stability. Ann. Probab. 7, 893-99.
15. WEI, C. and WINNICKI, J. (1990) Estimation of the mean in the branching process with immigration. Ann. Stat. 8, 1757-73.