Non-normal errors or nonlinearity? performance of unit root tests

ABSTRACT

This paper investigates how unit root tests that are designed for non-normal errors perform in the presence of unknown forms of nonlinearity. This allows us to examine whether any neglected nonlinearity in an estimation procedure could be reflected, at least partly, in the form of non-normality. Our simulation study shows that in general, univariate tests that exploit the information in non-normal errors remain relatively powerful compared to well-known nonlinear unit root tests under various forms of nonlinear alternatives. We also investigate the unit root properties of the real effective exchange rates and real interest rates for 60 countries. The results support the findings in the simulation that the neglected non-normality or nonlinearity in the existing tests is captured and used in the linearized testing procedures as a source of power improvement.

KEYWORDS:

• Unit root
• non-normality
• nonlinearity
• real effective exchange rates
• real interest rates

JEL CLASSIFICATION:

• C12
• C15
• C22

Acknowledgments

Authors appreciate Dr. Junsoo Lee, their mentor and advisor, for his insights and comments on this work.

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Notes

¹ Examples of widely adopted nonlinear unit-root tests are the momentum threshold autoregressive test of Enders and Granger (1998), the exponential smooth transition autoregressive nonlinear unit root tests of Kapetanios, Shin, and Snell (2003), the sign test of So and Shin (2001), and the inf-t test of Park and Shintani (2016) and those tests have been adopted to exploit the unit-root property of numerous real-time data.

² For related research, see Aas and Haff 2006), Bauwens and Laurent (2005), Hansen (1994), Jones and Faddy (2003), Patton (2004), and Venter and De Jongh (2002).

³ The exact formulation of each DGP is included in Table 1.

⁴ We do not include details for other tests. The reference sources for those can be widely found in the literature, e.g., Choi and Moh (2006, 2007) and Lee, Meng, and Lee (2011).

⁵ Throughout the paper, we focus on the regression with no time trend which is more compatible with many empirical topics of interest studying interest rates, unemployment rates, PPP hypothesis or the growth convergence.

⁶ For example, when T = 100, under the Generalized AR (1), the power of KSS, Sign, MTAR, and Inf-t are 0.40, 0.38, 0.36, and 0.43, respectively. In the same case, the power of the ADF test is 0.53.

⁷ For example, see Balke and Fomby (1997) and Enders and Granger (1998).

⁸ See Davies (1997).

⁹ For example, see Pippenger and Goering (1993, 2000).

¹⁰ For example, see Meng, Payne, and Lee (2013) and (2017).

¹¹ For another application of REER series, see Bahmani-Oskooee, Kutan, and Zhou (2007), Kruse (2011), Li and Park (2018), and Sarantis (1999).

¹² We use different data to investigate the small sample property instead of considering an arbitrarily chosen shorter time span of the REER data.