Asymptotic Distribution of an Estimator of the Boundary Parameter of an Unstable Process

Abstract

The limit distribution of the least squares estimator $\\hat{\\alpha}$ of the parameter $\\alpha$ of the first order stochastic difference equation, in the boundary case $|\\alpha| = 1$, is presented. With this, the asymptotic distributional problem for any real $\\alpha$ in the first order case is completely settled.