This chapter starts with a discussion of the motivation and scope of this book. Then, it introduces properties of unit root processes, relations between social science and unit roots, and some basic technical tools related to inferences on unit roots. It also provides an overview of subsequent chapters. Discussions on preliminary concepts and basic tools are brief because of the nature of this book, and the reader is referred to more specialized books such as Brockwell and Davis (1991), Davidson (1994), Hamilton (1994), Fuller (1976), and Serfling (1980).

Motivation and Scope of This Book

The last two decades or so have seen significant developments in the literature on unit roots. By the early 1980s, only a handful of papers had been written about unit roots, mostly by Professor Wayne Fuller and his coauthors. In those days, researchers in social science seldom used unit root tests for their empirical studies, and it was hard to find a graduate course on time series analysis offered by departments related to social science. Todays, the situation is radically different: there are many theoretical papers about unit roots, as the reference section of this book attests, and various procedures designed for testing for a unit root are often used in social science, particularly in economics. Naturally, commercial software for econometrics and statistics has incorporated many of the methods developed in the literature on unit roots.

Because so many unit root tests had been developed by the 1990s, some even thought that efforts dedicated to unit roots were excessive and unwarranted, as Maddala and Kim (1998, p. 488) succinctly quipped, “What we do not need is more unit root tests (each of which uses the Nelson–Plosser data as a guinea pig).” Nonetheless, because no one can predict with confidence the future direction of the world of knowledge, research on unit roots has continued to expand. The main vehicle for the massive theoretical developments in unit root regressions and testing has been the functional central limit theory (FCLT) that Phillips (1986, 1987a) first introduced to the literature on unit roots.