LOCAL ASYMPTOTIC-DISTRIBUTION RELATED TO THE AR(1) MODEL WITH DEPENDENT ERRORS

We consider the normalized least squares estimator of the parameter in a nearly integrated first-order autoregressive model with dependent errors. The dependence in the errors is modeled as either an MA(1) or an AR(1) process. As discussed in Perron (1991a), the usual asymptotic distribution is a poor guide to the finite sample distribution in the cases where (i) the MA root approaches -1 and (ii) the AR root approaches either 1 or -1. This occurs even for large sample sizes. This paper provides alternative asymptotic frameworks that treat the MA and AR roots as being local to their boundary. The appropriate limiting distributions and characteristic functions are derived allowing tabulation of distributional quantities via numerical integration. The results presented in this paper provide a better approximation to the finite sample distribution and help explain many of the finite sample results discussed in Perron (1991a).