# Testing for Unit Roots and the Impact of Quadratic Trends, with an Application to Relative Primary Commodity Prices

*David I. Harvey*,
*Stephen J. Leybourne* and
*Robert Taylor*

*Econometric Reviews*, 2011, vol. 30, issue 5, pages 514-547

**Abstract:**
In practice a degree of uncertainty will always exist concerning what specification to adopt for the deterministic trend function when running unit root tests. While most macroeconomic time series appear to display an underlying trend, it is often far from clear whether this component is best modeled as a simple linear trend (so that long-run growth rates are constant) or by a more complicated nonlinear trend function which may, for instance, allow the deterministic trend component to evolve gradually over time. In this article, we consider the effects on unit root testing of allowing for a local quadratic trend, a simple yet very flexible example of the latter. Where a local quadratic trend is present but not modeled, we show that the quasi-differenced detrended Dickey-Fuller-type test of Elliott et al. (1996) has both size and power which tend to zero asymptotically. An extension of the Elliott et al. (1996) approach to allow for a quadratic trend resolves this problem but is shown to result in large power losses relative to the standard detrended test when no quadratic trend is present. We consequently propose a simple and practical approach to dealing with this form of uncertainty based on a union of rejections-based decision rule whereby the unit root is rejected whenever either of the detrended or quadratic detrended unit root tests rejects. A modification of this basic strategy is also suggested which further improves on the properties of the procedure. An application to relative primary commodity price data highlights the empirical relevance of the methods outlined in this article. A by-product of our analysis is the development of a test for the presence of a quadratic trend which is robust to whether the data admit a unit root.

**Date:** 2011

**References:** Add references at CitEc

**Citations** View citations in EconPapers (7) Track citations by RSS feed

**Downloads:** (external link)

http://hdl.handle.net/10.1080/07474938.2011.553561 (text/html)

Access to full text is restricted to subscribers.

**Related works:**

Working Paper: Testing for unit roots and the impact of quadratic trends, with an application to relative primary commodity prices (2008)

This item may be available elsewhere in EconPapers: Search for items with the same title.

**Export reference:** BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text

**Persistent link:** http://EconPapers.repec.org/RePEc:taf:emetrv:v:30:y:2011:i:5:p:514-547

**Ordering information:** This journal article can be ordered from

http://www.tandfonline.com/pricing/journal/LECR20

Access Statistics for this article

Econometric Reviews is currently edited by *Dr. Essie Maasoumi*

More articles in Econometric Reviews from Taylor & Francis Journals

Series data maintained by ().