Limited Time Series with a Unit Root

44 Pages Posted: 6 Oct 2008

See all articles by Giuseppe Cavaliere

Giuseppe Cavaliere

University of Bologna - Department of Economics

Date Written: 2005


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 finitesample properties of the unit root statistics under range constraints.

Keywords: unit roots, limited time series, regulated Brownian motion

JEL Classification: C22

Suggested Citation

Cavaliere, Giuseppe, Limited Time Series with a Unit Root (2005). Econometric Theory, Vol. 21, No. 5, 2005, Available at SSRN: or

Giuseppe Cavaliere (Contact Author)

University of Bologna - Department of Economics ( email )

+390512098489 (Phone)

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