Selecting the Lag Length for the MGLS Unit Root Tests with Structural Change: A Warning Note for Practitioners Based on Simulations

This is a simulation-based warning note for practitioners who use the M G L S unit root tests in the context of structural change using different selection lag length criteria. With T = 100 , we find severe oversize problems when using some criteria, while other criteria produce an undersizing behavior. In view of this dilemma, we do not recommend using these tests. While such behavior tends to disappear when T = 250 , it is important to note that most empirical applications use smaller sample sizes such as T = 100 or T = 150 . The A D F G L S test does not present an oversizing or undersizing problem. The only disadvantage of the A D F G L S test arises in the presence of M A ( 1 ) negative correlation, in which case the M G L S tests are preferable, but in all other cases they are very undersized. When there is a break in the series, selecting the breakpoint using the Supremum method greatly improves the results relative to the Infimum method.

[1]  Michael Jansson,et al.  Improving Size and Power in the Unit Root Testing , 2005 .

[2]  Sebastian Fossati.  Covariate unit root tests with good size and power , 2012, Comput. Stat. Data Anal..

[3]  Serena Ng,et al.  A Note on the Selection of Time Series Models , 2005 .

[4]  J. Stock.  Unit roots, structural breaks and trends , 1986 .

[5]  Serena Ng,et al.  AN AUTOREGRESSIVE SPECTRAL DENSITY ESTIMATOR AT FREQUENCY ZERO FOR NONSTATIONARITY TESTS , 1998, Econometric Theory.

[6]  Serena Ng,et al.  Useful Modifications to some Unit Root Tests with Dependent Errors and their Local Asymptotic Properties , 1996 .

[7]  Paul Newbold,et al.  The balance between size and power in Dickey-Fuller tests with data-dependent rules for the choice of truncation lag , 1996 .

[8]  P. Perron,et al.  Further Evidence on Breaking Trend Functions in Macroeconomic Variables. , 1997 .

[9]  Josep Lluís Carrion‐i‐Silvestre,et al.  GLS-based unit root tests with multiple structural breaks both under the null and the alternative hypotheses , 2007 .

[10]  Pierre Perron,et al.  Dealing with Structural Breaks , 2005 .

[11]  G. Schwert,et al.  Tests for Unit Roots: a Monte Carlo Investigation , 1988 .

[12]  Paul Newbold,et al.  EMPIRICAL EVIDENCE ON DICKEY-FULLER-TYPE TESTS , 1992 .

[13]  Pierre Perron,et al.  A simple modification to improve the finite sample properties of Ng and Perron's unit root tests , 2007 .

[14]  Finite sample behaviour of the level shift model using quasi-differenced data , 2007 .

[15]  Tomás del Barrio Castro,et al.  THE IMPACT OF PERSISTENT CYCLES ON ZERO FREQUENCY UNIT ROOT TESTS , 2013, Econometric Theory.

[16]  P. Phillips,et al.  A Primer on Unit Root Testing , 1998 .

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

[18]  In Choi.  Almost All About Unit Roots , 2015 .

[19]  P. Phillips.  Testing for a Unit Root in Time Series Regression , 1988 .

[20]  Testing for unit roots in the possible presence of multiple trend breaks using minimum Dickey–Fuller statistics , 2013 .

[21]  Alok Bhargava,et al.  On the Theory of Testing for Unit Roots in Observed Time Series , 1986 .

[22]  Alastair R. Hall,et al.  Testing for a Unit Root in Time Series With Pretest Data-Based Model Selection , 1994 .

[23]  J. Stock,et al.  Efficient Tests for an Autoregressive Unit Root , 1992 .

[24]  Pierre Perron,et al.  Unit Root Tests Allowing for a Break in the Trend Function at an Unknown Time Under Both the Null and Alternative Hypotheses , 2009 .

[25]  P. Perron,et al.  Lag Length Selection and the Construction of Unit Root Tests with Good Size and Power , 2001 .

[26]  Pierre Perron,et al.  Additional Tests for a Unit Root Allowing for a Break in the Trend Function at an Unknown Time , 1998 .

[27]  Josep Lluís Carrion‐i‐Silvestre,et al.  GLS-BASED UNIT ROOT TESTS WITH MULTIPLE STRUCTURAL BREAKS UNDER BOTH THE NULL AND THE ALTERNATIVE HYPOTHESES , 2009, Econometric Theory.

[28]  Serena Ng,et al.  Unit Root Tests in ARMA Models with Data-Dependent Methods for the Selection of the Truncation Lag , 1995 .

[29]  T. B. Castro,et al.  On the Behaviour of Phillips–Perron Tests in the Presence of Persistent Cycles , 2015 .

[30]  Pierre Perron,et al.  GLS Detrending, Efficient Unit Root Tests and Structural Change , 2003 .