LIMITED TIME SERIES WITH A UNIT ROOT

By Giuseppe Cavaliere. Econometric Theory, 2005

126 citations recorded by the source corpus.

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.

Subfields: Finance

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Citations in the corpus

Testing for unit roots in bounded time series (2014, methodology): “Additionally, it is a key condition: (i) for establishing the asymptotic behavior of any unit root test statistics in the presence of bounds, see Cavaliere (2005), and (ii) for constructing proper unit root tests that take account of the bounds without making any parametric assumption on the…”
A Century of Shocks: The Evolution of the German City Size Distribution 1925-1999 (2008, unknown): “Note also that the presence of the bounds results in an overrejection of the unit root hypothesis (see Cavaliere, 2005 ).”