Brazilian Journal of Probability and Statistics

Estimation of parameters in the $\operatorname{DDRCINAR}(p)$ model

Xiufang Liu and Dehui Wang

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

This paper discusses a $p$th-order dependence-driven random coefficient integer-valued autoregressive time series model ($\operatorname{DDRCINAR}(p)$). Stationarity and ergodicity properties are proved. Conditional least squares, weighted least squares and maximum quasi-likelihood are used to estimate the model parameters. Asymptotic properties of the estimators are presented. The performances of these estimators are investigated and compared via simulations. In certain regions of the parameter space, simulative analysis shows that maximum quasi-likelihood estimators perform better than the estimators of conditional least squares and weighted least squares in terms of the proportion of within-$\Omega$ estimates. At last, the model is applied to two real data sets.

Article information

Source
Braz. J. Probab. Stat., Volume 33, Number 3 (2019), 638-673.

Dates
Received: March 2018
Accepted: May 2018
First available in Project Euclid: 10 June 2019

Permanent link to this document
https://projecteuclid.org/euclid.bjps/1560153855

Digital Object Identifier
doi:10.1214/18-BJPS405

Mathematical Reviews number (MathSciNet)
MR3960279

Keywords
Conditional least squares maximum quasi-likelihood $\operatorname{DDRCINAR}(p)$ model weighted conditional least squares asymptotic distribution

Citation

Liu, Xiufang; Wang, Dehui. Estimation of parameters in the $\operatorname{DDRCINAR}(p)$ model. Braz. J. Probab. Stat. 33 (2019), no. 3, 638--673. doi:10.1214/18-BJPS405. https://projecteuclid.org/euclid.bjps/1560153855


Export citation

References

  • Al-Osh, M. A. and Alzaid, A. A. (1987). First-order integer-valued autoregressive ($\operatorname{INAR}(1)$) process. Journal of Time Series Analysis 8, 261–275.
  • Alzaid, A. and Al-Osh, M. (1988). First-order integer-valued autoregressive ($\operatorname{INAR}(1)$) process: distributional and regression properties. Statistica Neerlandica 42, 53–61.
  • Alzaid, A. A. and Al-Osh, M. (1990). An integer-valued $p$th-order autoregressive structure ($\operatorname{INAR}(p)$) process. Journal of Applied Probability 27, 314–324.
  • Billingsley, P. (1961). Statistical Inference for Markov Processes. Chicago: University of Chicago Press.
  • Brännäs, K. and Hellström, J. (2001). Generalized integer-valued autoregression. Econometric Reviews 20, 425–443.
  • Brockwell, P. J. and Davis, R. A. (1987). Time Series: Theory and Methods. Media: Springer.
  • Cryer, J. D. and Chan, K. S. (2008). Time series analysis: With applications in R.
  • Davis, R. A., Dunsmuir, W. T. M. and Wang, Y. (1999). Modeling time series of count data. Statistics Textbooks and Monographs 158, 63–113.
  • Drost, F. C., Van Den Akker, R. and Werker, B. J. (2008). Local asymptotic normality and efficient estimation for $\operatorname{INAR}(p)$ models. Journal of Time Series Analysis 29, 783–801.
  • Drost, F. C., Van Den Akker, R. and Werker, B. J. (2009). Efficient estimation of auto-regression parameters and innovation distributions for semiparametric integer-valued $\operatorname{AR}(p)$ models. Journal of the Royal Statistical Society, Series B, Statistical Methodology 71, 467–485.
  • Du, J. G. and Li, Y. (1991). The integer-valued autoregressive ($\operatorname{INAR}(p)$) model. Journal of Time Series Analysis 12, 129–142.
  • Franke, J. and Seligmann, T. (1993). Conditional maximum likelihood estimates for $\operatorname{INAR}(1)$ processes and their application to modelling epileptic seizure counts. Developments in Time Series Analysis, 310–330.
  • Hall, P. and Heyde, C. C. (1980). Martingale Limit Theory and Its Applications. New York: Academic Press.
  • Hutton, J. E. and Nelson, P. I. (1986). Quasi-likelihood estimation for semimartingales. Stochastic Processes and Their Applications 22, 245–257.
  • Hwang, S. Y. and Basawa, I. V. (1998). Parameter estimation for generalized random coefficient autoregressive processes. Journal of Statistical Planning and Inference 68, 323–337.
  • Klimko, L. A. and Nelson, P. I. (1978). On conditional least squares estimation for stochastic processes. The Annals of Statistics 6, 629–642.
  • Latour, A. (1997). The multivariate $\operatorname{GINAR}(p)$ process. Advances in Applied Probability 29, 228–248.
  • Latour, A. (1998). Existence and stochastic structure of a non-negative integer-valued autoregressive process. Journal of Time Series Analysis 19, 439–455.
  • Li, C., Wang, D. and Zhang, H. (2015). First-order mixed integer-valued autoregressive processes with zero-inflated generalized power series innovations. Journal of the Korean Statistical Society 44, 232–246.
  • Li, Q., Lian, H. and Zhu, F. (2016). Robust closed-form estimators for the integer-valued $\operatorname{GARCH}(1,1)$ model. Computational Statistics & Data Analysis 101, 209–225.
  • Nicholls, D. F. and Quinn, B. G. (1982). Random Coefficient Autoregressive Models: An Introduction, Vol. 11. Springer Science and Business Media.
  • Steutel, F. W. and Van Harn, K. (1979). Discrete analogues of self-decomposability and stability. Annals of Probability 7, 893–899.
  • Zhang, H. and Wang, D. (2015). Inference for random coefficient $\operatorname{INAR}(1)$ process based on frequency domain analysis. Communications in Statistics Simulation and Computation 44, 1078–1100.
  • Zheng, H. and Basawa, I. V. (2008). First-order observation-driven integer-valued autoregressive processes. Statistics and Probability Letters 78, 1–9.
  • Zheng, H., Basawa, I. V. and Datta, S. (2006). Inference for $p$th-order random coefficient integer-valued autoregressive processes. Journal of Time Series Analysis 27, 411–440.
  • Zheng, H., Basawa, I. V. and Datta, S. (2007). First-order random coefficient integer-valued autoregressive processes. Journal of Statistical Planning and Inference 137, 212–229.
  • Zhu, R. and Joe, H. (2006). Modelling count data time series with Markov processes based on binomial thinning. Journal of Time Series Analysis 27, 725–738.
  • Zikun, W. (1965). Stochastic Process Theory. Beijing: Scientific Press.