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Smoothing Local-to-Moderate Unit Root Theory

By Peter C.B. Phillips, Tassos Magdalinos and Liudas Giraitis

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

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