Locally asymptotically optimal tests based on autoregression rank
scores are constructed for testing linear constraints on the structural
parameters of AR processes. Such tests are asymptotically distribution free and
do not require the estimation of nuisance parameters. They constitute robust,
flexible and quite powerful alternatives to existing methods such as the
classical correlogram-based parametric tests, the Gaussian Lagrange multiplier
tests, the optimal non-Gaussian and ranked residual tests described by
Kreiss, as well as to the aligned rank tests of Hallin and Puri. Optimality
requires a nontrivial extension of existing asymptotic representation results
to the case of unbounded score functions (such as the Gaussian quantile
function). The problem of testing AR$(p - 1)$ against AR$(p)$ dependence is
considered as an illustration. Asymptotic local powers and asymptotic relative
efficiencies are explicitly computed. In the special case of van der Waerden
scores, the asymptotic relative efficiency with respect to optimal
correlogram-based procedures is uniformly larger than one.