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Article

A new method of testing for a unit root in the INAR(1) model based on variances

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Pages 5915-5932 | Received 21 Jun 2018, Accepted 22 Jun 2020, Published online: 06 Jul 2020

References

  • Al-Osh, M. A., and A. A. Alzaid. 1987. First-order integer valued autoregressive (INAR(1)) process. Journal of Time Series Analysis 8 (3):261–75. doi:10.1111/j.1467-9892.1987.tb00438.x.
  • Alzaid, A. A., and M. A. Al-Osh. 1990. An integer-valued pth-order autoregressive structure(INAR(p) process. Journal of Applied Probability 27 (2):314–23. doi:10.2307/3214650.
  • Bakouch, H. S., M. Mohammadpour, and M. Shirozhan. 2018. A zero-inflated geometric INAR(1) process with random coefficient. Applications of Mathematics 63 (1):79–105. doi:10.21136/AM.2018.0082-17.
  • Bourguignon, M., J. Rodrigues, and M. Santos-Neto. 2019. Extended Poisson INAR(1) processes with equidispersion, underdispersion and overdispersion. Journal of Applied Statistics 46 (1):101–18. doi:10.1080/02664763.2018.1458216.
  • Bourguignon, M., and K. L. P. Vasconcellos. 2015. First order non-negative integer valued autoregressive processes with power series innovations. Brazilian Journal of Probability and Statistics 29 (1):71–93. doi:10.1214/13-BJPS229.
  • Brännäs, K., and J. Hellström. 1998. Forecasting based on very small samples and additional information. Umeå Economic Studies, Serial numbers. No. 472.
  • Brännäs, K., and J. Hellström. 1999. Generalized integer-valued autoregression. Umeå Economic Studies, Serial numbers. No. 501.
  • Bu, R., K. Hadri, and B. McCabe. 2008. Maximum likelihood estimation of higher-order integer-valued autoregressive process. Journal of Time Series Analysis 29 (6):973–94. doi:10.1111/j.1467-9892.2008.00590.x.
  • Dickey, D. A., and W. A. Fuller. 1979. Distribution of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association 74 (366):427–31. doi:10.2307/2286348.
  • Drost, F. C., R. van den Akker, and B. J. M. Werker. 2009. Efficient estimation of auto-regression parameters and innovation distributions for semiparametric integer-valued AR(p) models. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 71 (2):467–85. doi:10.1111/j.1467-9868.2008.00687.x.
  • Du, J., and Y. Li. 1991. The integer-valued autoregressive (INAR(p)) model. Journal of Time Series Analysis 12 :129–42.
  • Evans, G. B. A., and N. E. Savin. 1981. Testing for unit root 1. Econometrica 49 (3):753–79. doi:10.2307/1911521.
  • Freeland, R., and B. McCAbe. 2005. Asymptotic properties of CLS estimators in the Poisson AR(1) model. Statistics & Probability Letters 73 (2):147–53. doi:10.1016/j.spl.2005.03.006.
  • Haldrup, N., and S. Hylleberg. 1995. A note on the distribution of the least squares estimator of a random walk with drift: Some analytical evidence. Economics Letters 48 (3–4):221–28. doi:10.1016/0165-1765(94)00637-H.
  • Hamilton, J. D. 1994. Time Series Analysis. Princeton, NJ: Princeton University Press.
  • Hellström. J. 2001. Unit root testing in integer-valued AR(1) models. Economics Letters 70 :221–28.
  • Hylleberg, S., and G. E. Mizon. 1989. A note on the distribution of the least squares estimator of a random walk with drift. Economics Letters 29 (3):225–30. doi:10.1016/0165-1765(89)90065-7.
  • Kachour, M., and L. Truquet. 2011. A p-order signed integer-valued autoregressive (SINAR(p)) model. Journal of Time Series Analysis 32 (3):223–36. doi:10.1111/j.1467-9892.2010.00694.x.
  • Li, Y. 1990. The integer valued autoressiye model with dependence and stationary. Journal of the University of Petroleum (Science & Technology Edition) 14:115–25 (in Chinese).
  • Li, Y., J. Du, Y. Wu, and J. Shi. 1994. A type of seasonal integer-valued autoregressive model-sinar(1). Acta Mathematicae Applicatae-Sinica 17:100–108 (in Chinese).
  • Liu, L., and Y. Ma. 2010. Quality control chart for auto-correlated Poisson counts process. Journal of Systems Engineering 25:506–11 (in Chinese).
  • McKenzie, E. 1985. Some simple models for discrete variate time series. Journal of the American Water Resources Association 21 (4):645–50. doi:10.1111/j.1752-1688.1985.tb05379.x.
  • McKenzie, E. 1988. Some ARMA models for dependent sequences of Poisson counts. Advances in Applied Probability 20 (4):822–35. doi:10.1017/S0001867800018395.
  • Robert, C. J., and A. R. Tremayne. 2006. Binomial thinning models for integer time series. Statistical Modelling: An International Journal 6 (2):81–96. doi:10.1191/1471082X06st114oa.
  • Rudholm, N. 1999. Two essays on generic competition in the Swedish pharmaceuticals market. Umeå Economic Studies, Serial numbers. No. 485.
  • Shahiduzzaman Quoreshi, A. M. M. 2006. Long memory, count data, time series modelling for financial application. Umeå Economic Studies, Serial numbers. No. 673.
  • Shi, J. 2003. A type of seasonal integer-valued compound autoregressive model-SINCAR-SINCAR. Operations Research and Management Science 12:46–51 (in Chinese).
  • Steutel, F. W., and K. Van Harn. 1979. Discrete analogues of self-decomposability and stability. The Annals of Probability 7 (5):893–99. doi:10.1214/aop/1176994950.
  • Weiß, C. H. 2008. Serial dependence and regression of Poisson INARMA models. Journal of Statistics Plann Inference 138:2975–90.
  • Yu, K. 2011. Studies of modelling Discrete-valued Time Series and Its Applications. Cheng Du: Southwestern University of Finance and Economics.
  • Zheng, H., I. V. Basawa, and S. Datta. 2006. Inference for pth-order random coefficient integer-valued autoregresive processes. Journal of Time Series Analysis 27 (3):411–40. doi:10.1111/j.1467-9892.2006.00472.x.
  • Zheng, H., I. V. Basawa, and S. Datta. 2007. First-order random coefficient integer-valued autoregresive processes. Journal of Statistics Plann Inference 137 (1):212–29. doi:10.1016/j.jspi.2005.12.003.

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