A class of simple distribution-free rank-based unit root tests
Hallin,M. van den Akker,R. Werker,B.J.M.
Hallin,M.
van den Akker,R.
Werker,B.J.M.
Abstract
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 need 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 stressing asymptotic optimality, however, we emphasize finite-sample performances, which also depend, quite heavily, on 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 Elliott et al. (1996), Ng and Perron (2001), and Elliott and Müller (2006), for a broad range of initial values and for heavy-tailed innovation densities. Thus, they provide a useful complement to existing techniques.
Description
Appeared earlier as CentER Discussion Paper 2011-002
Date
2011
Journal Title
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Publisher
Research Projects
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Keywords
unit root, Dickey-Fuller test, local asymptotic normality, rank test, C12 - Hypothesis Testing: General, C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes
Citation
Hallin, M, van den Akker, R & Werker, B J M 2011, 'A class of simple distribution-free rank-based unit root tests', Journal of Econometrics, vol. 163, no. 2, pp. 200-214. < http://www.sciencedirect.com/science/article/pii/S0304407611000698 >