CFDP 1659

Smoothing Local-to-Moderate Unit Root Theory


Publication Date: May 2008

Pages: 17


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.


Edgeworth expansion, Local to unity, Moderate deviations, Unit root distribution

JEL Classification Codes:  C22

See CFP: 1309