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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
Download reference. The following formats are available: HTML (with abstract), plain text (with abstract), BibTeX, RIS (EndNote, RefMan, ProCite), ReDIF
Handle: RePEc:cup:etheor:v:21:y:2005:i:05:p:907-945_05

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Cited by:
  1. Giuseppe Cavaliere, 2005. "Testing mean reversion in target-zone exchange rates," Applied Economics, Taylor and Francis Journals, vol. 37(20), pages 2335-2347.
  2. 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.
  3. 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).
  4. 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.
  5. 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.

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