Whittle likelihood estimation in INAR(1) process

Abstract

The frequency domain analysis is considered in the stationary INAR(1) process under a general innovation. The Whittle likelihood from the demeaned data is shown to be not identifiable with respect to the innovation mean and variance. Using an identifiable version of the Whittle likelihood, the strong consistency and asymptotic normality of the Whittle estimator are established. Furthermore, the Wald-type test about the equidispersion is proposed on the basis of the estimators for the innovation mean and variance.

KEYWORDS:

• Whittle likelihood
• frequency domain analysis
• INAR(1) process
• test of equidispersion

Acknowledgments

The author is grateful to two reviewers for their comments. Also, the author would like to express my gratitude to Professor Yoshihide Kakizawa, Hokkaido University, for his advice on this work, together with careful guidance during the preparation of the manuscript.

Disclosure statement

The corresponding author states that there is no conflict of interest.

Additional information

Funding

The author acknowledges financial support from China Scholarship Council.