S. Nabeya et P. Perron, LOCAL ASYMPTOTIC-DISTRIBUTION RELATED TO THE AR(1) MODEL WITH DEPENDENT ERRORS, Journal of econometrics, 62(2), 1994, pp. 229-264
Citations number
30
Categorie Soggetti
Social Sciences, Mathematical Methods",Economics,"Mathematical, Methods, Social Sciences
We consider the normalized least squares estimator of the parameter in
a nearly integrated first-order autoregressive model with dependent e
rrors. The dependence in the errors is modeled as either an MA(1) or a
n 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 approac
hes either 1 or -1. This occurs even for large sample sizes. This pape
r provides alternative asymptotic frameworks that treat the MA and AR
roots as being local to their boundary. The appropriate limiting distr
ibutions and characteristic functions are derived allowing tabulation
of distributional quantities via numerical integration. The results pr
esented in this paper provide a better approximation to the finite sam
ple distribution and help explain many of the finite sample results di
scussed in Perron (1991a).