%0 Journal Article
%T Understanding the Functional Central Limit Theorems with Some Applications to Unit Root Testing with Structural Change El Teorema del L¨ªmite Central Funcional con algunas aplicaciones a ra¨ªces unitarias con cambios estructurales
%A Juan Carlos Aquino
%A Gabriel Rodr¨ªguez
%J Revista Econom¨ªa
%D 2013
%I Pontificia Universidad Cat¨®lica del Per¨²
%X The 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. Hoy en d¨ªa es una pr¨¢ctica est¨¢ndar de trabajo emp¨ªrico la aplicaci¨®n de diferentes estad¨ªsticos de contraste de ra¨ªz unitaria. A pesar de ser un aspecto pr¨¢ctico, estos estad¨ªsticos poseen distribuciones complejas y no est¨¢ndar que dependen de funcionales de ciertos procesos estoc¨¢sticos y sus derivaciones representan una barrera incluso para varios econometristas te¨®ricos. Estas derivaciones est¨¢n basadas en herramientas estad¨ªsticas fundamentales y rigurosas que no son (muy) bien conocidas por econometristas est¨¢ndar. El presente art¨ªculo completa esta brecha al explicar en una forma simple una de estas herramientas fundamentales la cual es el Teorema del L¨ªmite Central Funcional. Por lo tanto, este documento analiza los fundamentos y la aplicabilidad de dos versiones del Teorema del L¨ªmite Central Funcional dentro del marco de una ra¨ªz unitaria con un quiebre estructural. La atenci¨®n inicial se centra en la estructura probabil¨ªstica de las series de tiempo propuesta por Phillips (1987a), la cual es aplicada por Perron (1989) para estudiar los efectos de un qu
%K Prueba de Ra¨ªz Unitaria
%K Quiebre Estructural
%K Teorema del L¨ªmite Central Funcional
%K Proceso Ornstein-Uhlenbeck
%U http://revistas.pucp.edu.pe/index.php/economia/article/view/6379