:: Volume 16, Issue 2 (3-2020) ::
JSRI 2020, 16(2): 287-317 Back to browse issues page
A New Integer-Valued AR(1) Process Based on Power Series Thinning Operator
Eisa Mahmoudi 1, Ameneh Rostami , Rasoul Rouzegar
1- , emahmoudi@yazd.ac.ir
Abstract:   (1251 Views)
Abstract: In this paper, we introduce the first-order non-negative integer-valued autoregressive (INAR(1)) process with Poisson-Lindley innovations based on a new thinning operator called power series thinning operator. Some statistical properties of process are given. The unknown parameters of the model are estimated by three methods; the conditional least squares, Yule-Walker and conditional maximum likelihood. Then, the performances of these estimators are evaluated using simulation study. Three special cases of model are investigated in some detail. Finally, the model is applied to four real data sets, such as the annual number of earthquakes, the monthly number of measles cases, the numbers of sudden death series and weekly counts of the incidence of acute febrile muco-cutaneous lymph node syndrome. Then we show the potentiality of the model.
 
Keywords:  Integer-valued autoregressive processes, power series distributions, Poisson-Lindley distribution, thinning operator, Yule-Walker equations.
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Type of Study: Research | Subject: General
Received: 2020/10/12 | Accepted: 2021/02/22 | Published: 2021/09/19
References
1. Aghababaei Jazi, M.A., Jones, G., and Lai, C.D. (2012). Integer-Valued AR(1) with Geometric Innovations. Journal of the Iran Statistical Society, 11, 173-190.
2. Al-Osh, M.A., and Alzaid, A.A. (1987). First-Order Integer-Valued Autoregressive (INAR(1)) Process. Journal of Time Series Analysis, 8, 261-275. [DOI:10.1111/j.1467-9892.1987.tb00438.x]
3. Bourguignon, M., and Vasconcellos, K.L. (2015). First-Order Non-Negative Integer-Valued Autoregressive Processes with Power Series Innovations. Brazilian Journal of Probability and Statistics, 29, 71-93. [DOI:10.1214/13-BJPS229]
4. Du, J., and Li, Y. (1991). The Integer Valued Autoregressive (INAR(p)) Model. Journal of Time Series Analysis, 12, 129-142. [DOI:10.1111/j.1467-9892.1991.tb00073.x]
5. Ferland, R., Latour, A., and Oraichi, D. (2006). Integer-Valued GARCH Processes. Journal of Time Series Analysis, 27, 923-942. [DOI:10.1111/j.1467-9892.2006.00496.x]
6. Livio, T., Mamode Khan, N., Bourguignon, M., and Bakouch, H.S. (2018). An INAR(1) Model with Poisson-Lindley Innovations. Economics Bulletin, 38, 1505-1513.
7. Mohammadpour, M., Bakouch, H.S., and Shirozhan, M. (2018). Poisson-Lindley INAR(1) Model with Applications. Brazilian Journal of Probability and Statistics, 32, 262-280. [DOI:10.1214/16-BJPS341]
8. Ristic, M.M., Bakouch, H.S., and Nastic, A.S. (2009). A New Geometric First Order Integer-Valued Autoregressive (NGINAR(1)) Process. Statistical Planning and Inference, 139, 2218-2226. [DOI:10.1016/j.jspi.2008.10.007]
9. Sankaran, M. (1970). The Discrete Poisson-Lindley Distribution, vol. 26. Biometrics, Washington, pp. 145-149. [DOI:10.2307/2529053]
10. Schweer, S., and Weiss, C.H. (2014). Compound Poisson INAR(1) Processes: Stochastic Properties and Testing for Over Dispersion. Computational Statistics and Data Analysis, 77, 267-284. [DOI:10.1016/j.csda.2014.03.005]
11. Steutel, F.W., and van Harn, K. (1979). Discrete Analogues of Self Decomposability and Stability. The Annals of Probability, 7, 893-899. [DOI:10.1214/aop/1176994950]

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