Understanding the functional central limit theorems with some applications to unit root testing with structural change
AbstractThe application of different unit root statistics is by now a standard practice in empirical work. Even when it is a practical issue, these statistics have complex nonstandard distributions depending on functionals of certain stochastic processes, and their derivations represent a barrier even for many theoretical econometricians. These derivations are based on rigorous and fundamental statistical tools which are not (very) well known by standard econometricians. This paper aims to fill this gap by explaining in a simple way one of these fundamental tools: namely, the Functional Central Limit Theorem. To this end, this paper analyzes the foundations and applicability of 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. Thereafter, attention is focused 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 Rodriguez (2003), which extends the Generalized Least Squares detrending approach due to Elliot et al. (1996). An empirical application is provided.
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Bibliographic InfoArticle provided by Departamento de Economía - Pontificia Universidad Católica del Perú in its journal Revista Economia.
Volume (Year): 36 (2013)
Issue (Month): 71 ()
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More information through EDIRC
Unit root testing; structural break; functional central limit theorem; Ornstein-Uhlenbeck process.;
Other versions of this item:
- Juan Carlos Aquino & Gabriel Rodríguez, 2011. "Understanding The Functional Central Limit Theorems With Some Applications To Unit Root Testing With Structural Change," Documentos de Trabajo, Departamento de EconomÃa - Pontificia Universidad CatÃ³lica del PerÃº 2011-319, Departamento de Economía - Pontificia Universidad Católica del Perú.
- C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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