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Limited Time Series With A Unit Root

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  • Cavaliere, Giuseppe

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 analyses are applied to time series that 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 sample 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. Because deviations from the standard unit root theory are measured through two noncentrality parameters that can be consistently estimated, simple measures of the impact of range constraints on the asymptotic distributions are obtained. Generalizations of standard unit root tests that are robust to the presence of range constraints are also provided. Finally, it is shown that the proposed asymptotic framework provides an adequate approximation to the finite-sample properties of the unit root statistics under range constraints.Partial financial support from Italian MIUR grants is gratefully acknowledged. I thank, without implicating, Pentti Saikkonen (the co-editor), an anonymous referee, Attilio Gardini, Martin Jacobsen, Robert de Jong, Paolo Paruolo, Anders Rahbek, and participants at the 58th European Meeting of the Econometric Society, Stockholm, August 21 24, 2003, for helpful comments. I also thank the Bank of International Settlements for providing the European monetary system exchange rate data.

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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 21 (2005)
Issue (Month): 05 (October)
Pages: 907-945

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Handle: RePEc:cup:etheor:v:21:y:2005:i:05:p:907-945_05

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Cited by:
  1. 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.
  2. 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).
  3. 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.
  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. Giuseppe Cavaliere, 2005. "Testing mean reversion in target-zone exchange rates," Applied Economics, Taylor & Francis Journals, vol. 37(20), pages 2335-2347.
  6. Granger, Clive W.J., 2010. "Some thoughts on the development of cointegration," Journal of Econometrics, Elsevier, vol. 158(1), pages 3-6, September.
  7. 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.
  8. Helmut Herwartz & Fang Xu, 2009. "Panel data model comparison for empirical saving-investment relations," Applied Economics Letters, Taylor & Francis Journals, vol. 16(8), pages 803-807.
  9. Cavaliere, Giuseppe & Xu, Fang, 2014. "Testing for unit roots in bounded time series," Journal of Econometrics, Elsevier, vol. 178(P2), pages 259-272.
  10. Niklas Potrafke, 2014. "The Evidence on Globalization," CESifo Working Paper Series 4708, CESifo Group Munich.
  11. Ferris, J.S. & Park, S. & Winer, S.L., 2007. "Studying the Role of Political Competition in the Evolution of Government Size Over Long Horizons," Cambridge Working Papers in Economics 0774, Faculty of Economics, University of Cambridge.
  12. 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.
  13. 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.
  14. 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.
  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. 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.

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