# Lund University Publications

## LUND UNIVERSITY LIBRARIES

### 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)
author
organization
publishing date
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
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}},
}

```