TY - UNPB
T1 - A Class of Simple Distribution-free Rank-based Unit Root Tests (Revision of DP 2010-72)
AU - Hallin, M.
AU - van den Akker, R.
AU - Werker, B.J.M.
N1 - Subsequently published in the Journal of Econometrics (2011)
Pagination: 36
PY - 2011
Y1 - 2011
N2 - We propose a class of distribution-free rank-based tests for the null hypothesis of a unit root. This class is indexed by the choice of a reference density g, which needs not coincide with the unknown actual innovation density f. The validity of these tests, in terms of exact finite sample size, is guaranteed, irrespective of the actual underlying density, by distribution-freeness. Those tests are locally and asymptotically optimal under a particular asymptotic scheme, for which we provide a complete analysis of asymptotic relative efficiencies. Rather than asymptotic optimality, however, we emphasize finitesample performances. Finite-sample performances of unit root tests, however, depend quite heavily on initial values. We therefore investigate those performances as a function of initial values. It appears that our rank-based tests significantly outperform the traditional Dickey-Fuller tests, as well as the more recent procedures proposed by Elliot, Rothenberg, and Stock (1996), Ng and Perron (2001), and Elliott and M¨uller (2006), for a broad range of initial values and for heavy-tailed innovation densities. As such, they provide a useful complement to existing techniques.
AB - We propose a class of distribution-free rank-based tests for the null hypothesis of a unit root. This class is indexed by the choice of a reference density g, which needs not coincide with the unknown actual innovation density f. The validity of these tests, in terms of exact finite sample size, is guaranteed, irrespective of the actual underlying density, by distribution-freeness. Those tests are locally and asymptotically optimal under a particular asymptotic scheme, for which we provide a complete analysis of asymptotic relative efficiencies. Rather than asymptotic optimality, however, we emphasize finitesample performances. Finite-sample performances of unit root tests, however, depend quite heavily on initial values. We therefore investigate those performances as a function of initial values. It appears that our rank-based tests significantly outperform the traditional Dickey-Fuller tests, as well as the more recent procedures proposed by Elliot, Rothenberg, and Stock (1996), Ng and Perron (2001), and Elliott and M¨uller (2006), for a broad range of initial values and for heavy-tailed innovation densities. As such, they provide a useful complement to existing techniques.
KW - Unit root
KW - Dickey-Fuller test
KW - Local Asymptotic Normality
KW - Rank test
M3 - Discussion paper
VL - 2011-002
T3 - CentER Discussion Paper
BT - A Class of Simple Distribution-free Rank-based Unit Root Tests (Revision of DP 2010-72)
PB - Faculteit der Economische Wetenschappen
CY - TILBURG
ER -