The Effect of Recursive Detrending on Panel Unit Root Tests
(2015) In Journal of Econometrics 185(2). p.453-467- Abstract
- This paper analyzes the properties of panel unit root tests based on recursively detrended
data. The analysis is conducted while allowing for a (potentially) non-linear
trend function, which represents a more general consideration than the current state of
affairs with (at most) a linear trend. A new test statistic is proposed whose asymptotic
behavior under the unit root null hypothesis, and the simplifying assumptions of a polynomial
trend and iid errors is shown to be surprisingly simple. Indeed, the test statistic is
not only asymptotically independent of the true trend polynomial, but is in fact unique
in that it is independent also of the degree of the fitted polynomial.... (More) - This paper analyzes the properties of panel unit root tests based on recursively detrended
data. The analysis is conducted while allowing for a (potentially) non-linear
trend function, which represents a more general consideration than the current state of
affairs with (at most) a linear trend. A new test statistic is proposed whose asymptotic
behavior under the unit root null hypothesis, and the simplifying assumptions of a polynomial
trend and iid errors is shown to be surprisingly simple. Indeed, the test statistic is
not only asymptotically independent of the true trend polynomial, but is in fact unique
in that it is independent also of the degree of the fitted polynomial. However, this invariance
property does not carry over to the local alternative, under which it is shown that
local power is a decreasing function of the trend degree. But while power does decrease,
the rate of shrinking of the local alternative is generally constant in the trend degree,
which goes against the common belief that the rate of shrinking should be decreasing in
the trend degree. The above results are based on simplifying assumptions. To compensate
for this lack of generality, a second, robust, test statistic is proposed, whose validity
does not require that the trend function is a polynomial or that the errors are iid. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/4588923
- author
- Westerlund, Joakim LU
- organization
- publishing date
- 2015
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Unit root test, Polynomial trend function, Recursive detrending., Deterministic trend, Panel data
- in
- Journal of Econometrics
- volume
- 185
- issue
- 2
- pages
- 453 - 467
- publisher
- Elsevier
- external identifiers
-
- wos:000350778500011
- scopus:84922720721
- ISSN
- 0304-4076
- DOI
- 10.1016/j.jeconom.2014.06.015
- language
- English
- LU publication?
- yes
- id
- bead9aa8-94e9-4f0c-b125-51606e29e7dd (old id 4588923)
- date added to LUP
- 2016-04-01 10:26:59
- date last changed
- 2022-01-25 23:20:37
@article{bead9aa8-94e9-4f0c-b125-51606e29e7dd,
abstract = {{This paper analyzes the properties of panel unit root tests based on recursively detrended<br/><br>
data. The analysis is conducted while allowing for a (potentially) non-linear<br/><br>
trend function, which represents a more general consideration than the current state of<br/><br>
affairs with (at most) a linear trend. A new test statistic is proposed whose asymptotic<br/><br>
behavior under the unit root null hypothesis, and the simplifying assumptions of a polynomial<br/><br>
trend and iid errors is shown to be surprisingly simple. Indeed, the test statistic is<br/><br>
not only asymptotically independent of the true trend polynomial, but is in fact unique<br/><br>
in that it is independent also of the degree of the fitted polynomial. However, this invariance<br/><br>
property does not carry over to the local alternative, under which it is shown that<br/><br>
local power is a decreasing function of the trend degree. But while power does decrease,<br/><br>
the rate of shrinking of the local alternative is generally constant in the trend degree,<br/><br>
which goes against the common belief that the rate of shrinking should be decreasing in<br/><br>
the trend degree. The above results are based on simplifying assumptions. To compensate<br/><br>
for this lack of generality, a second, robust, test statistic is proposed, whose validity<br/><br>
does not require that the trend function is a polynomial or that the errors are iid.}},
author = {{Westerlund, Joakim}},
issn = {{0304-4076}},
keywords = {{Unit root test; Polynomial trend function; Recursive detrending.; Deterministic trend; Panel data}},
language = {{eng}},
number = {{2}},
pages = {{453--467}},
publisher = {{Elsevier}},
series = {{Journal of Econometrics}},
title = {{The Effect of Recursive Detrending on Panel Unit Root Tests}},
url = {{http://dx.doi.org/10.1016/j.jeconom.2014.06.015}},
doi = {{10.1016/j.jeconom.2014.06.015}},
volume = {{185}},
year = {{2015}},
}