A small sample confidence interval for autoregressive parameters

This paper is concerned with interval estimation of an autoregressive parameter when the parameter space allows for magnitudes outside the unit interval. In this case, intervals based on the least-squares estimator tend to require a high level of numerical computation and can be unreliable for small sample sizes. Intervals based on the asymptotic distribution of instrumental variable estimators provide an alternative. If the instrument is taken to be the sign function, the interval is centered at the Cauchy estimator and a large sample interval can be created by estimating the standard error of this estimator. The interval proposed in this paper avoids estimating this standard error and results in a small sample improvement in coverage probability. In fact, small sample coverage is exact when the innovations come from a normal distribution.