Generalized Rank Estimates For An Autoregressive Time Series: A U-Statistic Approach

A class of weighted rank-based estimates for estimating the parameter vector of an autoregressive time series is considered. This class of estimates is similar to, and contains, the class proposed by Terpstra et al. 54]. Asymptotic linearity properties are derived for the so called GR-estimates. Based on these properties, the GR-estimates are shown to be asymptotically normal at rate n ^1/2. The theory of U-statistics along with a characterization of weak dependence that is inherent in stationary AR(p) models are the primary tools used to obtain the results. The so called pair-wise slopes estimator, which is a special case of this class of estimates, is discussed in an AR(1) context. This revised version was published online in June 2006 with corrections to the Cover Date.