COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1659 Smoothing Local-to-Moderate Unit Root Theory Peter C.B. Phillips, Tassos Magdalinos and Liudas Giraitis May 2008 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. |
