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\centerline{\bf STANFORD UNIVERSITY}
\centerline{\bf DEPARTMENT OF STATISTICS}
\centerline{\big DEPARTMENTAL SEMINAR}
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\centerline{4:15 p.m., Tuesday, May 22, 2001}
\centerline{Sequoia Hall Rm. 200}
\centerline{(Cookies at 3:45 in 1st Floor Lounge)}

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\centerline{\sl Dimitris N. Politis}
\centerline{\sl Department of Mathematics}
\centerline{\sl University of California, San Diego}
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\centerline{\bf Unit Roots, Cointegration, and the Continuous-Path 
Block-Bootstrap}

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The problem of nonparametric resampling in the context of time series that
are suspected to be integrated and/or cointegrated is described.  A
nonparametric block bootstrap  procedure is proposed for  testing for a
unit root. The resampling   procedure is based on weak assumptions on the
dependence structure of the process, and successfully generates unit root
integrated pseudo-series retaining the important characteristics of the
data. As a consequence the procedure can accurately capture the
distribution of many unit root test statistics proposed in the literature.
Large sample theory is developed and the asymptotic validity of the block
bootstrap-based unit root testing is shown via a bootstrap functional 
limit
theorem. Applications to some  particular test statistics of the unit root
hypothesis, e.g., least squares and Dickey-Fuller type  statistics are
given. Time permitting, the problem of testing for cointegration will also
be discussed.

(this is joint work with E. Paparoditis, Univ. of Cyprus)
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