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

Abstract

We present a new method of testing for unit roots in the INAR(1) model based on estimated variances. We present detailed simulation evidence regarding the performance of the new test statistics that show that our method is more powerful than the Dickey–Fuller tests especially in nearly unit root circumstances. We evaluate the presence of a unit root in two empirical time series, namely, the number of schools for the blind, deaf, and the developmentally disabled people as well as the number of teachers in such schools. We find evidence of a unit root in either series.

KEYWORDS:

• Discrete-valued time series
• Integer-valued autoregression model
• Non-stationary time series
• Testing based on variances
• Unit root test

AMS CLASSIFICATION:

• 62M10
• 60J80
• 62F12

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Acknowledgements

The authors would like to thank Editor in Chief and two referees for careful reading of the paper and a number of perceptive and beneficial comments which improved it greatly.

Additional information

Funding

The research of the first author was supported by the Opening Project of Sichuan Province University Key Laboratory of Bridge Non-destruction Detecting and Engineering Computing (2018QZJ01), and the talent introduction project of Sichuan University of Science & Engineering (2019RC10).