  An autoregressive-moving average model in which all roots of the
autoregressive polynomial are reciprocals of roots of the moving average
polynomial and vice versa is called an all-pass time series model. All-pass
models are useful for identifying and modeling noncausal and noninvertible
autoregressive-moving average processes. We establish asymptotic normality and
consistency for rank-based estimators of all-pass model parameters. The
estimators are obtained by minimizing the rank-based residual dispersion
function given by Jaeckel [Ann. Math. Statist. 43 (1972) 1449--1458]. These
estimators can have the same asymptotic efficiency as maximum likelihood
estimators and are robust. The behavior of the estimators for finite samples is
studied via simulation and rank estimation is used in the deconvolution of a
simulated water gun seismogram.
