THE ADEQUACY OF ASYMPTOTIC APPROXIMATIONS IN THE NEAR-INTEGRATED AUTOREGRESSIVE MODEL WITH DEPENDENT ERRORS

We consider the normalized least squares estimator of the parameter in a nearly integrated first-order autoregressive model with dependent e rrors, In a first step we consider its asymptotic distribution as well as asymptotic expansion up to order O-p(T-1). We derive a limiting mo ment generating function which enables us to calculate various distrib utional quantities by numerical integration. A simulation study is per formed to assess the adequacy of the asymptotic distribution when the errors are correlated. We focus our attention on two leading cases: MA (1) errors and AR(1) errors. The asymptotic approximations are shown t o be inadequate as the MA root gets close to -1 and as the AR root app roaches either -1 or 1, Our theoretical analysis helps to explain and understand the simulation results of Schwert (1989) and DeJong, Nanker vis, Savin, and Whiteman (1992) concerning the size and power of Phill ips and Perron's (1988) unit root test, A companion paper, Nabeya and Perron (1994), presents alternative asymptotic frameworks in the cases where the usual asymptotic distribution fails to provide an adequate approximation to the finite-sample distribution.