A new model of near integration is formulated in
which the local to unity parameter is identifiable and
consistently estimable with time series data. The properties
of the model are investigated, new functional laws for
near integrated time series are obtained that lead to mixed
diffusion processes, and consistent estimators of the localizing
parameter are constructed. The model provides a more complete
interface between I(0) and I(1) models than
the traditional local to unity model and leads to autoregressive
coefficient estimates with rates of convergence that vary continuously
between the O(√n) rate of stationary autoregression,
the O(n) rate of unit root regression, and the
power rate of explosive autoregression. Models with deterministic
trends are also considered, least squares trend regression is shown
to be efficient, and consistent estimates of the localizing
parameter are obtained for this case also. Conventional unit root
tests are shown to be consistent against local alternatives in the
new class.
HOW TO ESTIMATE AUTOREGRESSIVE ROOTS NEAR UNITY
