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Discussion Paper

Limit Theory for Moderate Deviations from a Unit Root under Weak Dependence

An asymptotic theory is given for autoregressive time series with weakly dependent innovations and a root of the form ρn = 1 + c/nα, involving moderate deviations from unity when α in (0,1) and c in R are constant parameters. The limit theory combines a functional law to a diffusion on D[0,∞) and a central limit theorem. For c > 0, the limit theory of the first-order serial correlation coefficient is Cauchy and is invariant to both the distribution and the dependence structure of the innovations.