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Limited time series with a unit root

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  • Giuseppe Cavaliere

Abstract

This paper develops an asymptotic theory for integrated and near-integrated time series whose range is constrained in some ways. Such a framework arises when integration and cointegration analysis are applied to persistent series which are bounded either by construction or because they are subject to control. The asymptotic properties of some commonly used integration tests are discussed; the bounded unit root distribution is introduced to describe the limiting distribution of the first-order autoregressive coefficient of a random walk under range constraints. The theoretical results show that the presence of such constraints can lead to drastically different asymptotics. Since deviations from the standard unit root theory are measured through noncentrality parameters, simple measures of the impact of range constraints on the asymptotic distributions are obtained. Finally, the proposed asymptotic framework provides an extremely adequate approximation of the finite sample properties of the unit root statistics under range constraints.

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Bibliographic Info

Paper provided by Department of Statistics, University of Bologna in its series Quaderni di Dipartimento with number 1.

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Date of creation: 2003
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Handle: RePEc:bot:quadip:88

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Cited by:
  1. Ott, Herve, 2012. "Which factors drive which volatility in the grain sector?," 123rd Seminar, February 23-24, 2012, Dublin, Ireland 122486, European Association of Agricultural Economists.
  2. Maarten Bosker & Steven Brakman & Harry Garretsen & Marc Schramm, 2006. "A Century of Shocks: The Evolution of the German City Size Distribution 1925 – 1999," CESifo Working Paper Series 1728, CESifo Group Munich.
  3. Herwartz, Helmut & Xu, Fang, 2006. "Panel data model comparison for empirical saving-investment relations," Economics Working Papers 2006,06, Christian-Albrechts-University of Kiel, Department of Economics.
  4. Casalin, Fabrizio, 2013. "Testing the expectations hypothesis of the term structure with permanent-transitory component models," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 3192-3203.
  5. Atkinson, Anthony B. & Leigh, Andrew, 2010. "The Distribution of Top Incomes in Five Anglo-Saxon Countries over the Twentieth Century," IZA Discussion Papers 4937, Institute for the Study of Labor (IZA).
  6. Carrion-i-Silvestre, Josep Lluís & Gadea, María Dolores, 2013. "GLS-based unit root tests for bounded processes," Economics Letters, Elsevier, vol. 120(2), pages 184-187.
  7. Carlo V. FIORIO & Simon MOHUN & Roberto VENEZIANI, 2013. "Social Democracy and Distributive Conflict in the UK, 1950-2010," Departmental Working Papers 2013-09, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano, revised 16 May 2013.
  8. Niklas Potrafke, 2014. "The Evidence on Globalization," CESifo Working Paper Series 4708, CESifo Group Munich.
  9. J. Ferris & Soo-Bin Park & Stanley Winer, 2008. "Studying the role of political competition in the evolution of government size over long horizons," Public Choice, Springer, vol. 137(1), pages 369-401, October.
  10. Nielsen, Heino Bohn, 2009. "Comment on "The long-run determinants of UK wages, 1860-2004"," Journal of Macroeconomics, Elsevier, vol. 31(1), pages 29-34, March.
  11. Giuseppe Cavaliere, 2005. "Testing mean reversion in target-zone exchange rates," Applied Economics, Taylor & Francis Journals, vol. 37(20), pages 2335-2347.
  12. Granger, Clive W.J., 2010. "Some thoughts on the development of cointegration," Journal of Econometrics, Elsevier, vol. 158(1), pages 3-6, September.
  13. Niels Haldrup & Robinson Kruse & Timo Teräsvirta & Rasmus T. Varneskov, 2012. "Unit roots, nonlinearities and structural breaks," CREATES Research Papers 2012-14, School of Economics and Management, University of Aarhus.
  14. Cavaliere, Giuseppe & Xu, Fang, 2014. "Testing for unit roots in bounded time series," Journal of Econometrics, Elsevier, vol. 178(P2), pages 259-272.
  15. Herwartz, Helmut & Xu, Fang, 2006. "Reviewing the sustainability/stationarity of current account imbalances with tests for bounded integration," Economics Working Papers 2006,07, Christian-Albrechts-University of Kiel, Department of Economics.
  16. Davies, Antony, 2009. "Human development and the optimal size of government," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 38(2), pages 326-330, March.

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