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

  • Juan Carlos Aquino
  • Gabriel Rodríguez


    (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)

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

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Length: pages
Date of creation: 2011
Date of revision:
Publication status: published
Handle: RePEc:pcp:pucwps:wp00319
Contact details of provider: Postal: Av. Universitaria 1801, San Miguel, Lima, Perú
Phone: (511) 626-2000 ext. 4950, 4951
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  1. Anindya Banerjee & Robin L. Lumsdaine & James H. Stock, 1990. "Recursive and Sequential Tests of the Unit Root and Trend Break Hypothesis: Theory and International Evidence," NBER Working Papers 3510, National Bureau of Economic Research, Inc.
  2. Eric Zivot & Donald W.K. Andrews, 1990. "Further Evidence on the Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Cowles Foundation Discussion Papers 944, Cowles Foundation for Research in Economics, Yale University.
  3. 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.
  4. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037, July.
  5. 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.
  6. Peter C.B. Phillips, 1986. "Regression Theory for Near-Integrated Time Series," Cowles Foundation Discussion Papers 781R, Cowles Foundation for Research in Economics, Yale University, revised Jan 1987.
  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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