Real-count data time series often show the phenomenon of over-dispersion. In this paper, we introduce the first-order integer-valued autoregressive process with seasonal structure. The univariate marginal distribution is derived from the Delaporte distribution and the innovations are convolution of Poisson with α-fold zero modified geometric distribution, based on binomial thinning operator, for modeling integer-valued time series with over-dispersion. Some properties of the model are derived. The methods of Yule-Walker, conditional least squares, and conditional maximum likelihood are used to estimate the parameters. The Monte Carlo experiment is conducted to evaluate the performances of these estimators in finite samples. At the end, this model is illustrated using a real data set and is compared to some INAR(1) models.
Shalbaf, M., Parham, G., & Chinipardaz, R. (2024). A seasonal Integer-Valued AR(1) model with delaporte marginal distribution. Journal of Advanced Mathematical Modeling, 14(3-English), 16-40. doi: 10.22055/jamm.2024.45842.2246
MLA
Maryam Shalbaf; Gholamali Parham; Rahim Chinipardaz. "A seasonal Integer-Valued AR(1) model with delaporte marginal distribution". Journal of Advanced Mathematical Modeling, 14, 3-English, 2024, 16-40. doi: 10.22055/jamm.2024.45842.2246
HARVARD
Shalbaf, M., Parham, G., Chinipardaz, R. (2024). 'A seasonal Integer-Valued AR(1) model with delaporte marginal distribution', Journal of Advanced Mathematical Modeling, 14(3-English), pp. 16-40. doi: 10.22055/jamm.2024.45842.2246
VANCOUVER
Shalbaf, M., Parham, G., Chinipardaz, R. A seasonal Integer-Valued AR(1) model with delaporte marginal distribution. Journal of Advanced Mathematical Modeling, 2024; 14(3-English): 16-40. doi: 10.22055/jamm.2024.45842.2246
)