Smooth transitions, asymmetric adjustment and unit roots

Abstract

The aim of this article is to develop a unit root test that takes into account two sources of nonlinearites in data, i.e. asymmetric speed of mean reversion and structural changes. The asymmetric speed of mean reversion is modelled by means of a exponential smooth transition autoregression (ESTAR) function for the autoregressive parameter, whereas structural changes are approximated by a smooth transition in the deterministic components. We find that the proposed test performs well in terms of size and power, in particular when the autoregressive parameter is near unity.

Keywords:

• unit roots
• nonlinear trends
• exponential smooth transition autoregressive model
• structural change

JEL Classification:

• C12
• C32

Funding

The authors gratefully acknowledge the MICINN (Ministerio de Ciencia e Innovación, Spain) research grant ECO2011-30260-C03-01.

Disclaimer Statement

The usual disclaimer applies.

Notes

¹ Note that the test proposed in this section is a more general version of these authors’ tests, since we do not restrict the intercept to be equal at the beginning and at the end of the sample.

² Note that the function takes values between 0 and 1. In the limiting case with , changes almost instantaneously from 0 to 1.

³ These authors only consider the cases of an intercept and a linear trend.

⁴ The RATS code to obtain the critical values for other sample sizes is available upon request.