Testing for a Unit Root against Transitional Autoregressive Models
Working Paper No. 05-W10
Joon Y. Park and Mototsugu Shintani
ABSTRACT [article]
This paper considers the test of a unit root in transitional
autoregressive models. In particular, we develop the asymptotic theory
of the inf-t test for the null hypothesis of a unit root in a wide
class of nonlinear autoregressive models having parameters that are
identified only under the alternative of stationarity. Our framework
is very general and allows for virtually all potentially interesting
models with the threshold, discrete and smooth transition
functions. The specifications of shortrun dynamics used in the paper
are also fully general, and comparable to those used in the linear
unit root models. Most importantly, our asymptotics take it into
consideration that the parameter space has a random limit. This is an
essential feature of the unit root test in transitional autoregressive
models, which has been ignored in the literature. For this very
general class of transitional autoregressive models, we show that the
inf-t test has well-defined limit distribution depending only upon
the transition function and the limit parameter space. The critical
values of the test are provided for some of the commonly used models
under the conventional specification of the parameter space. Our
simulation study shows that the test has good size with the power that
is significantly higher than the usual ADF test even for samples of
relatively small sizes. We apply the test to various economic time
series and find strong evidence for the rejection of random walks in
favor of stationary transitional autoregressive models.
Keywords and Phrases: Unit root test, threshold autoregressive models (TAR),
logistic and exponential smooth transition autoregressive models (LSTAR
and ESTAR)
JEL Classification Numbers: C12, C16, C22