Unit root tests and their challenges

Abstract

The Dickey-Fuller test (DF test) and its various modified versions have been widely used for unit root or random walk testing, though advices are necessary regarding their proper use in hands-on statistical algorithm software. In this paper, we review the development of such tests over several decades. We examine why such modified versions of DF tests were developed and proper instructions regarding their use are essential. In addition, we discuss a simple way to overcome this hurdle.

Key Words:

• extended MA($\infty$) model
• persistency parameter
• DF test

Acknowldegements

We are grateful to the anoymous referee for his/her valuable comments.

Funding

C. Park’s work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (NRF-2019R1F1A1058723). S.Y. Hwang’s work was supported by a grant from the National Research Foundation of Korea (NRF-2021R1F1A1047952). J. Ha’s work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. 2021R1F1A1062879). TY Kim’s work was supported by a grant from the National Research Foundation of Korea (NRF-2019R1F1A1060152).

Notes

1 In the simulation, we used adfTest with type=‘nc’ option (no constant and no time trend) in fUnitRoots package with lag k = 0 for the DF test and lag $k={(n-1)}^{1/3}$ for the ADF test, respectively.

Additional information

Funding

C. Park’s work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (NRF-2019R1F1A1058723). S.Y. Hwang’s work was supported by a grant from the National Research Foundation of Korea (NRF-2021R1F1A1047952). J. Ha’s work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. 2021R1F1A1062879). TY Kim’s work was supported by a grant from the National Research Foundation of Korea (NRF-2019R1F1A1060152).