Maximum likelihood estimation of the DDRCINAR(p) model

Abstract

In this paper, the novel estimating methods and their properties for pth-order dependence-driven random coefficient integer-valued autoregressive time series model (DDRCINAR(p)) are studied as the innovation sequence has a Poisson distribution and the thinning is binomial. Strict stationarity and ergodicity for DDRCINAR(p) model are proved. Conditional maximum likelihood and conditional least squares are used to estimate the model parameters. Asymptotic normality of the proposed estimators are derived. Finite sample properties of the conditional maximum likelihood estimator are examined in relation to the widely used conditional least squares estimator. It is concluded that, if the Poisson assumption can be justified, conditional maximum likelihood method performs better in terms of bias and MSE. Finally, three real data sets are analyzed to demonstrate the practical relevance of the model.

Keywords:

• Conditional least squares
• conditional maximum likelihood
• DDRCINAR(p) model
• asymptotic distribution

Acknowledgements

Authors are very grateful to editor and referee for their careful reading and valuable comments which have greatly improved this paper. Thank you all for helping me writing this LATEX sample file.

Additional information

Funding

This work is supported by National Natural Science Foundation of China (No. 11871028, 11731015, 11901053), Natural Science Foundation of Jilin Province (No. 20180101216JC), and Program for Changbaishan Scholars of Jilin Province (2015010).