73
Views
0
CrossRef citations to date
0
Altmetric
Articles

Efficient estimation in (PINAR(1)) model: semiparametric case

&
Pages 7110-7132 | Received 17 Oct 2019, Accepted 14 Sep 2020, Published online: 04 Oct 2020

References

  • Al-Osh, M., and A. A. Alzaid. 1987. First order integer-valued autoregressive (INAR(1)) processes. Journal of Time Series Analysis 8 (3):261–75. doi:10.1111/j.1467-9892.1987.tb00438.x.
  • Alzaid, A. A., and M. Al-Osh. 1990. Integer-valued p th-order autoregressive structure (INAR(p)) process. Journal of Applied Probability 27 (2):314–24. doi:10.2307/3214650.
  • Bentarzi, M., and L. Djeddou. 2014. Adaptive estimation of periodic first-order threshold autoregressive model. Communications in Statistics - Simulation and Computation 43 (7):1611–30. doi:10.1080/03610918.2012.740123.
  • Bentarzi, M., H. Guerbyenne, and M. Merzougui. 2009. Adaptive estimation of causal periodic autoregressive model. Communications in Statistics - Simulation and Computation 38 (8):1592–609. doi:10.1080/03610910903061006.
  • Bentarzi, M., and M. Hallin. 1996. Locally optimal tests against periodic autoregression. Econometric Theory 12 (1):88–112. doi:10.1017/S0266466600006459.
  • Bickel, P. J. 1982. On adaptive estimation. The Annals of Statistics 10 (3):647–71. doi:10.1214/aos/1176345863.
  • Bickel, P. J., C. A. J. Klaassen, and J. A. Wellner. 1998. Efficient and adaptive estimation for semiparametric models. 2nd ed. Berlin: Springer.
  • Billingsley, P. 1995. Measure and probability. New York: John Wiley and Sons.
  • Bourguignon, M., K. L. P. Vasconcellos, V. A. Reisen, and M. Ispany. 2016. A Poisson (INAR(1)) process with a seasonal structure. Journal of Statistical Computation and Simulation 86 (2):373–87. doi:10.1080/00949655.2015.1015127.
  • Brännäs, K., and A. Hall. 2001. Estimation in integer-valued moving average models. Applied Stochastic Models in Business and Industry 17 (3):277–91. doi:10.1002/asmb.445.
  • Drost, C., R. van den Akker, and B. Werker. 2008. Local asymptotic normality and efficient estimation for INAR(p) models. Journal of Time Series Analysis 29 (5):783–801. doi:10.1111/j.1467-9892.2008.00581.x.
  • Drost, C., R. van den Akker, and B. 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.-G., and Y. Li. 1991. The integer-valued autoregressive (INAR(p)) model. Journal of Time Series Analysis 12:129–42.
  • Fabian, V., and J. Hannan. 1982. On estimation and adaptive estimation for locally asymptotically normal families. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 59 (4):459–78. doi:10.1007/BF00532803.
  • Ferland, R., A. Latour, and D. Oraichi. 2006. Integer-valued GARCH process. Journal of Time Series Analysis 27 (6):923–42. doi:10.1111/j.1467-9892.2006.00496.x.
  • Fokianos, K. 2012. Count time series models. In Handbook of Statistics. Time Series Analysis: Methods and Applications, ed. T. S. Rao, S. Subba Rao, and C.R. Rao, vol. 30, 315–47. Elsevier.
  • Freeland, R. K. 1998. Statistical analysis of discrete-time series with applications to the analysis of workers compensation claims data. PhD thes., University of British Columbia.
  • Gladyshev, E. G. 1963. Periodically and almost-periodically correlated random processes with continuous time parameter. Theory of Probability & Its Applications 8 (2):173–77. doi:10.1137/1108016.
  • Hájek, J. 1972. Local asymptotic minimax and admissibility in estimation. Proceeding of Sixth Berkeley Symposium on Mathematical Statistics and Probability. Berkeley, CA: University of California Press, vol. 1, 175–94.
  • Koul, H. L., and A. Schick. 1996. Adaptive estimation in a random coefficient autoregressive model. The Annals of Statistics 24 (3):1025–52.
  • Kreiss, J. P. 1987. On adaptative estimation in stationary ARMA processes. The Annals of Statistics 15 (1):112–33.
  • Le Cam, L. 1960. Locally asymptotically normal families of distributions. University of California Publications in Statistics 3:37–98.
  • Monteiro, M., M. G. Scotto, and I. Pereira. 2010. Integer-valued autoregressive process with periodic structure. Journal of Statistical Planning and Inference 140 (6):1529–41. doi:10.1016/j.jspi.2009.12.015.
  • Sadoun, M., and M. Bentarzi. 2020. Efficient estimation in periodic INAR(1) model: Parametric case. Communications in Statistics-Simulation and Computation 49 (8):2014–34. doi:10.1080/03610918.2018.1510524.
  • Stein, C. 1956. Efficient nonparametric testing and estimation. In Proceeding of the Third Berkeley Sympsium on Mathematical Statistic and Probability. Berkley, CA: University of California Press, vol. 1, 187–96.
  • Steutel, F. W., and K. Van Harn. 1979. Discrete analogues of self-decomposability and stability. The Annals of Probability 7 (5):893–9. doi:10.1214/aop/1176994950.
  • Van Der Vaart, A. W. 1991. On differentiable functionals. The Annals of Statistics 19 (1):178–204. doi:10.1214/aos/1176347976.
  • Van Der Vaart, A. W. 1995. Efficiency of infinite dimensional M- estimators. Statistica Neerlandica 49 (1):9–30. doi:10.1111/j.1467-9574.1995.tb01452.x.
  • Van Der Vaart, A. W. 2000. Asymptotic statistics. 1st ed. Cambridge: Cambridge University Press.
  • Van Der Vaart, A. W., and J. A. Wellner. 1993. Weak convergence and empirical process. 2nd ed. New York: Springer.
  • Van Der Vaart, A. W., and J. A. Wellner. 2007. Empirical processes indexed by estimated functions. Institute of Mathematical Statistics Lecture Notes - Monograph Series 55:234–52.
  • Wald, A. 1943. Tests of statistical hypotheses concerning several parameters when the number of observations is large. Transactions of the American Mathematical Society 54 (3):426–82. doi:10.1090/S0002-9947-1943-0012401-3.
  • Zhu, R., and H. Joe. 2006. Modelling count data time series with Markov processes based on binomial thinning. Journal of Time Series Analysis 27 (5):725–38. doi:10.1111/j.1467-9892.2006.00485.x.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.