An invariant sign test for random walks based on recursive median adjustment

Beong Soo So, Dong Wan Shin

Research output: Contribution to journalArticlepeer-review

28 Scopus citations


We propose a new invariant sign test for random walks against general stationary processes and develop a theory for the test. In addition to the exact binomial null distribution of the test, we establish various important properties of the test: the consistency against a wide class of possibly nonlinear stationary autoregressive conditionally heteroscedastic processes and/or heavy-tailed errors; a local asymptotic power advantage over the classical Dickey-Fuller test; and invariance to monotone data transformations, to conditional heteroscedasticity and to heavy-tailed errors. Using the sign test, we also investigate various interrelated issues such as M-estimator, exact confidence interval, sign test for serial correlation, robust inference for a cointegration model, and discuss possible extensions to models with autocorrelated errors. Monte-Carlo experiments verify that the sign test has not only very stable sizes but also locally better powers than the parametric Dickey-Fuller test and the nonparametric tests of Granger and Hallman (1991. Journal of Time Series Analysis 12, 207-224) and Burridge and Guerre (1996. Econometric Theory 12, 705-719) for heteroscedastic and/or heavy tailed errors.

Original languageEnglish
Pages (from-to)197-229
Number of pages33
JournalJournal of Econometrics
Issue number2
StatePublished - Jun 2001

Bibliographical note

Funding Information:
The authors are greatly indebted to an associate editor, two referees, and Professor Yoon-Jae Whang for many constructive comments on the earlier version of this paper. This research was supported by a grant for BK-21 project from Korea Research Foundation.


  • Heteroscedasticity
  • Nonlinear transformation
  • Nonparametric sign test


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