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.     

Bounded Area Tests For Comparing The Dynamics Between ARMA Processes

This article presents a new test for discerning whether or not two independent autoregressive moving average (ARMA) processes have the same autocovariance structure. This test utilizes a specific geometric feature of a time series plot, namely the area bounded between the line segments that connect adjacent points and the time axis. It will be shown that if you sample two ARMA processes and calculate the magnitudes of the two resulting bounded areas, then a significant difference among these areas tends to imply a significant difference in autocovariances.