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Understanding The Functional Central Limit Theorems With Some Applications To Unit Root Testing With Structural Change

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  • Juan Carlos Aquino
  • Gabriel Rodríguez

    ()
    (Departamento de Economía - Pontificia Universidad Católica del Perú)

Abstract

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)

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Bibliographic Info

Paper provided by Departamento de Economía - Pontificia Universidad Católica del Perú in its series Documentos de Trabajo with number 2011-319.

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Length: pages
Date of creation: 2011
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Publication status: published
Handle: RePEc:pcp:pucwps:wp00319

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Web page: http://www.pucp.edu.pe/departamento/economia/
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Keywords: Hypothesis Testing; Unit Root; Structural Break; Functional Central Limit Theorem; Weak Convergence; Wiener Process; Ornstein-Uhlenbeck Process;

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  1. Zivot, Eric & Andrews, Donald W K, 2002. "Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 25-44, January.
  2. Bhargava, Alok, 1986. "On the Theory of Testing for Unit Roots in Observed Time Series," Review of Economic Studies, Wiley Blackwell, vol. 53(3), pages 369-84, July.
  3. Banerjee, Anindya & Lumsdaine, Robin L & Stock, James H, 1992. "Recursive and Sequential Tests of the Unit-Root and Trend-Break Hypotheses: Theory and International Evidence," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 271-87, July.
  4. Phillips, Peter C B, 1988. "Regression Theory for Near-Integrated Time Series," Econometrica, Econometric Society, vol. 56(5), pages 1021-43, September.
  5. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
  6. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037.
  7. Sargan, John Denis & Bhargava, Alok, 1983. "Testing Residuals from Least Squares Regression for Being Generated by the Gaussian Random Walk," Econometrica, Econometric Society, vol. 51(1), pages 153-74, January.
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Cited by:
  1. Aquino, Juan Carlos & Espino, Freddy, 2013. "Terms of Trade and Current Account Fluctuations: a Vector Autoregression Approach," Working Papers 2013-008, Banco Central de Reserva del Perú.
  2. Gabriel Rodríguez & Alfredo Vargas, 2011. "Impacto de Expectativas Políticas en los Retornos del Indice General de la Bolsa de Valores de Lima," Documentos de Trabajo 2011-323, Departamento de Economía - Pontificia Universidad Católica del Perú.

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