Limited time series with a unit root
AbstractThis 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.
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Bibliographic InfoPaper provided by Department of Statistics, University of Bologna in its series Quaderni di Dipartimento with number 1.
Date of creation: 2003
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