Limited time series with a unit root

Cavaliere, Giuseppe (2003) Limited time series with a unit root. Bologna, IT: Dipartimento di Scienze Statistiche "Paolo Fortunati", Alma Mater Studiorum Università di Bologna, p. 44. DOI 10.6092/unibo/amsacta/2420. In: Quaderni di Dipartimento. Serie Ricerche ISSN 1973-9346.
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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.

Document type
Monograph (Working Paper)
Cavaliere, Giuseppe
Deposit date
21 Feb 2008
Last modified
16 May 2011 12:07

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