Title

Smoothing Local-to-Moderate Unit Root Theory

Document Type

Discussion Paper

Publication Date

5-1-2008

CFDP Number

1659

CFDP Pages

17

Abstract

A limit theory is established for autoregressive time series that smooths the transition between local and moderate deviations from unity and provides a transitional form that links conventional unit root distributions and the standard normal. Edgeworth expansions of the limit theory are given. These expansions show that the limit theory that holds for values of the autoregressive coefficient that are closer to stationarity than local (i.e. deviations of the form = 1 + (c/n), where n is the sample size and c < 0) holds up to the second order. Similar expansions around the limiting Cauchy density are provided for the mildly explosive case.

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