Review and Application of Two Integer – Valued Time Series Models

Document Type : Scientific Research

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Abstract

This paper first introduces Delaporte and first type Luders Formel models. Then these models are considered as stationary marginal distributions for first-order integer – valued autoregressive processes. After that, the higher order integer - valued autoregressive processes are considered. Various features of these models such as regressive behavior, time reversible and etc. are studied. Also Simulation studies for study of sample paths in these models were done. Finally, the model parameters were estimated and the two models are compared via a real data set.
 

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References

[1] Al-Osh, M.A. and Alzaid, A.A. (1987). First-order integer-valued autoregressive  (INAR (1)) process. Journal of Time Series Analysis, 8(3), 261-275..
[2] Delaporte, P. (1959). Quelques probl´emes de statistique math´ematique pos´es par`I assurance automobile et le bonus non sinistre. Bulletin Trimestriel de l’lnstitut desActuaires Franc¸ais, 227, 87-102.
[3] Lawrance, A.J. (1978). Some Autoregressive models for point processes. In Colloquia Mathematica Societatis Janos Bolyai, 24, 257-275.
[4] Luders, R. (1934). Die Statistik der seltenen Ereignisse. Biometrika, 26, 108-128.

[5] Jose, K. K., and Thomas, M.M. (2011). Generalized Laplacian distributions and autoregressive processes. Communications in Statistics-Theory and Methods, 40 (23), 4263-4277.

Volume 2, Issue 2 - Serial Number 1
February 2017
Pages 67-73

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