UNDERSTANDING THE FUNCTIONAL CENTRAL LIMIT THEOREMS WITH SOME APPLICATIONS TO UNIT ROOT TESTING WITH STRUCTURAL CHANGE
Juan Aquino () and
Gabriel Rodríguez ()
No 2011-319, Documentos de Trabajo / Working Papers from Departamento de Economía - Pontificia Universidad Católica del Perú
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 e¢ ciency issues is introduced by Perron and RodrÌguez (2003), which extends the Generalized Least Squares detrending approach due to Elliott, Rothenberg, and Stock (1996)
Keywords: Hypothesis Testing; Unit Root; Structural Break; Functional Central Limit Theorem; Weak Convergence; Wiener Process; Ornstein-Uhlenbeck Process (search for similar items in EconPapers)
JEL-codes: C12 C22 (search for similar items in EconPapers)
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Journal Article: Understanding the functional central limit theorems with some applications to unit root testing with structural change (2013)
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