Understanding the Functional Central Limit Theorems with Some Applications to Unit Root Testing with Structural Change

This paper analyzes and employs two versions of the Functional Central Limit Theorem within the framework of a unit root with a structural break. Initial attention is focused on the probabilistic structure of the time series to be considered. Later, attention is placed on the asymptotic theory for nonstationary time series proposed by Phillips (1987a), which is applied by Perron (1989) to study the effects of an (assumed) exogenous structural break on the power of the augmented Dickey-Fuller test and by Zivot and Andrews (1992) to criticize the exogeneity assumption and propose a method for estimating an endogenous breakpoint. A systematic method for dealing with efficiency issues is introduced by Perron and Rodríguez (2003), which extends the Generalized Least Squares detrending approach due to Elliott, Rothenberg, and Stock (1996)

Keywords
Functional Central Limit Theorem, Hypothesis Testing, Ornstein-Uhlenbeck Process, Structural Break, Unit Root, Weak Convergence

JEL Classification

C12 C22