Rank-based unit root testing in the presence of structural change under the null: simulation results and an application to US inflation

The size distortion of the Dickey-Fuller (Journal of the American Statistical Association, 74, pp. 427–31, 1979) unit root test is examined in the presence of structural changes in both the level and variance of integrated time series. In contrast to previous studies, the empirically relevant situation in which such breaks occur simultaneously is examined. It is shown that the severe distortion observed for the Dickey-Fuller test can be dramatically reduced via application of a simple rank-based method. The simulation results presented are supported by an empirical examination of the integrated nature of US inflation where differing inferences are drawn using the Dickey-Fuller test and the rank-based Dickey-Fuller test.

[1]  Chang‐Jin Kim,et al.  Has the U.S. Economy Become More Stable? A Bayesian Approach Based on a Markov-Switching Model of the Business Cycle , 1999, Review of Economics and Statistics.

[2]  Paul Newbold,et al.  Spurious rejections by Dickey-Fuller tests in the presence of a break under the null , 1998 .

[3]  Paul Newbold,et al.  Unit root tests with a break in innovation variance , 2002 .

[4]  D. Andrews,et al.  Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis , 1992 .

[5]  C. Inclan,et al.  Volatility in Emerging Stock Markets , 1997, Journal of Financial and Quantitative Analysis.

[6]  Paul Newbold,et al.  Behaviour of the standard and symmetric Dickey–Fuller‐type tests when there is a break under the null hypothesis , 2000 .

[7]  P. Perron,et al.  The Great Crash, The Oil Price Shock And The Unit Root Hypothesis , 1989 .

[8]  A. M. Robert Taylor,et al.  Variance Shifts, Structural Breaks, and Stationarity Tests , 2003 .

[9]  Clive W. J. Granger,et al.  NONLINEAR TRANSFORMATIONS OF INTEGRATED TIME SERIES , 1991 .

[10]  Dick van Dijk,et al.  Testing for Volatility Changes in U.S. Macroeconomic Time Series , 2004, Review of Economics and Statistics.

[11]  Margaret Mary McConnell,et al.  Output Fluctuations in the United States: What Has Changed Since the Early 1980s? , 1998 .

[12]  Stephen J. Leybourne,et al.  TESTING FOR UNIT ROOTS USING FORWARD AND REVERSE DICKEY‐FULLER REGRESSIONS , 1995 .

[13]  W. Fuller,et al.  Distribution of the Estimators for Autoregressive Time Series with a Unit Root , 1979 .

[14]  P. Perron,et al.  Testing For A Unit Root In A Time Series With A Changing Mean , 1990 .

[15]  J. Stock,et al.  Recursive and Sequential Tests of the Unit Root and Trend Break Hypothesis: Theory and International Evidence , 1990 .