Unit Roots and Structural Breaks

This special issue deals with problems related to unit roots and structural change, and the interplay between the two. The research agenda dealing with these topics have proven to be of importance for devising procedures that are reliable for inference and forecasting. Several important contributions have been made. Still, there is scope for improvements and analyses of the properties of existing procedures. This special issue provides contributions that follow up on what has been done and/or offer new perspectives on such issues and related ones. Both theoretical and applied papers are included. I briefly outline the papers, grouping them by themes. Structural Change—Theory. Cheol-Keun Cho and Timothy J. Vogelsang consider testing for structural change when serial correlation may be present in the errors of the regression, in which case a common practice is to use a heteroscedasticity and autocorrelation robust Wald test. Following important work by Vogelsang and co-authors (e.g., Kiefer and Vogelsang (2015)), a fixed-bandwidth theory is developed to provide better approximations for the test statistics. It is shown to improve upon the standard asymptotic distribution theory, whereby the bandwidth is negligible compared to the sample size; e.g., Andrews (1993), Bai and Perron (1998, 2003). Jingjing Yang considers the consistency of trend break point estimators when the number of breaks is underspecified. As shown in Bai (1997) and Bai and Perron (1998), with stationary variables, if a one-break model is estimated when multiple breaks exist, then the estimate of the break fraction converges to one of the true break fractions (the one that minimizes the overall sum of squared residuals). Interestingly, she shows this to not be the case when considering breaks in a linear trend function. This result suggests that the application of the Kejriwal and Perron (2010) extension of the Perron and Yabu (2009) test should be applied with caution. Aparna Sengupta considers the problem of testing for a structural break in the spatial lag parameter in a panel model (spatial autoregressive). She proposes a likelihood ratio test and derives its limit distribution when both the number of individual units N and the number of time periods T is large or N is fixed and T is large. A break date estimator is also proposed. Unit Root and Trend Break—Theory. Ricardo Quineche and Gabriel Rodríguez provide interesting further finite sample simulation results about the tests proposed by Perron and Rodriguez (2003), who extended the work of Perron (1989, 1997), Zivot and Andrews (1992), and Vogelsang and Perron (1998), among others. They show that the MGLS versions suggested by Ng and Perron (2001) suffer from severe size distortions when using the so-called “infimum method” to select the break date (i.e., minimizing the t-statistic of the sum of the autoregressive coefficients) and common methods to select the autoregressive lag order. This occurs whether a break is present or not. On the other hand, when using the “supremum method” (i.e., minimizing the sum of squared residuals from the trend-break regression), this problem only holds when no break is present. These results point to the usefulness of the methods advocated by Kim and Perron (2009) and Carrión-i-Silvestre et al. (2009). Fractional integration—Theory. Seong Yeon Chang and Pierre Perron consider testing procedures for the null hypothesis of a unit root process against the alternative of a fractional process, called a fractional unit root test. They extend the Lagrange Multiplier (LM) tests of Robinson (1994) and Tanaka (1999) to allow for a slope change in trend with or without a concurrent level shift under both the null and alternative hypotheses. Building on the work of Chang and Perron