TY - JOUR
T1 - An invariant sign test for random walks based on recursive median adjustment
AU - So, Beong Soo
AU - Shin, Dong Wan
N1 - 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.
PY - 2001/6
Y1 - 2001/6
N2 - 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.
AB - 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.
KW - Heteroscedasticity
KW - Nonlinear transformation
KW - Nonparametric sign test
UR - http://www.scopus.com/inward/record.url?scp=0346312270&partnerID=8YFLogxK
U2 - 10.1016/S0304-4076(01)00053-7
DO - 10.1016/S0304-4076(01)00053-7
M3 - Article
AN - SCOPUS:0346312270
SN - 0304-4076
VL - 102
SP - 197
EP - 229
JO - Journal of Econometrics
JF - Journal of Econometrics
IS - 2
ER -